# Glossary > Definitions of the reinsurance and cat-modelling terms used on this site, from AAL to YELT, with notation and links to the pages that treat them in depth. Source: https://reinsurance.dev/glossary/ This glossary defines the domain terms used across the site and points at the page that treats each in depth; the site's operating rules are indexed separately on [Scope, conventions & assumptions](https://reinsurance.dev/conventions/). An entry gives the definition, the notation where the term has one, the sentence that separates the term from its nearest neighbour, and links; worked examples and derivations stay on the page named under **Discussed in**. A name the site does not use for a term it does define (AAL, PLT, slip, underwriting cycle) has a one-line entry that points at the site's headword. --- ## A ### AAL (Average Annual Loss) Vendor language for [expected loss (EL)](https://reinsurance.dev/glossary/#el-expected-loss). ### AEP (Aggregate Exceedance Probability) EP curve based on the total (aggregate) loss per trial across all occurrences in a period. Contrasts with [OEP](https://reinsurance.dev/glossary/#oep-occurrence-exceedance-probability), which uses only the largest single occurrence loss. **Discussed in:** [Exceedance probability curves](https://reinsurance.dev/toolkit/distributions/#oep-vs-aep) ### Aggregate Deductible The total loss a [cedent](https://reinsurance.dev/glossary/#cedent) must absorb across all occurrences in a period before reinsurance responds. Unlike an occurrence-level attachment, an aggregate deductible accumulates losses across occurrences. It is the attachment $A$ of an [aggregate excess](https://reinsurance.dev/financial-modelling/terms/aggregate-excess/) term. **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/#occurrence-vs-aggregate) (conceptual), [Aggregate excess](https://reinsurance.dev/financial-modelling/terms/aggregate-excess/) (formal) ### Aggregate Excess A financial term that applies an attachment $A$ and a limit $\ell$ to a [trial's](https://reinsurance.dev/glossary/#trial) running total instead of to each occurrence, written $\text{agg}_{\text{excess}}(A, \ell)$: per trial, $\min(\max(\sum_{(t,e)} L_{j,t,e}^{\text{subject}} - A, 0), \ell)$. Its output stays a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) because each occurrence row carries its [erosion](https://reinsurance.dev/glossary/#erosion) of the layer, in claims order. The [occurrence excess](https://reinsurance.dev/glossary/#occurrence-excess) applies the same layer to each occurrence independently. **See also:** [Occurrence Excess](https://reinsurance.dev/glossary/#occurrence-excess), [Erosion](https://reinsurance.dev/glossary/#erosion), [Aggregate Limit](https://reinsurance.dev/glossary/#aggregate-limit), [Aggregate Deductible](https://reinsurance.dev/glossary/#aggregate-deductible), [Term](https://reinsurance.dev/glossary/#term-financial-term) **Discussed in:** [Aggregate excess](https://reinsurance.dev/financial-modelling/terms/aggregate-excess/), [AggXoL](https://reinsurance.dev/financial-modelling/contracts/aggxol/) ### Aggregate Limit The cap on what a contract pays across a whole [trial](https://reinsurance.dev/glossary/#trial): the $\ell$ of an [aggregate excess](https://reinsurance.dev/glossary/#aggregate-excess). A [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss) always carries one, because $n$ [reinstatements](https://reinsurance.dev/glossary/#reinstatement) cap the period's recoveries at $(1 + n) \cdot \ell$. Contrast the [event limit](https://reinsurance.dev/glossary/#event-limit), which caps each occurrence. **This site's convention:** a quota share's annual limit caps the subject aggregate before the cession, as the event limit does; filed wordings cap the reinsurer's share, and a ceded-side annual limit $\ell$ is the subject-side limit $\ell_a = \ell / q$. **See also:** [Limit](https://reinsurance.dev/glossary/#limit), [Event Limit](https://reinsurance.dev/glossary/#event-limit), [Aggregate Deductible](https://reinsurance.dev/glossary/#aggregate-deductible) **Discussed in:** [Dissecting a contract](https://reinsurance.dev/financial-modelling/dissection/), [AggXoL](https://reinsurance.dev/financial-modelling/contracts/aggxol/), [Quota share](https://reinsurance.dev/financial-modelling/contracts/quota-share/#with-annual-limit) ### Aggregate Stop Loss A reinsurance contract that caps the cedent's total annual losses above an [aggregate deductible](https://reinsurance.dev/glossary/#aggregate-deductible): the same structure this site models as an [AggXoL](https://reinsurance.dev/glossary/#aggxol-aggregate-excess-of-loss), whose entry states what separates the two names. **See also:** [AggXoL](https://reinsurance.dev/glossary/#aggxol-aggregate-excess-of-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [AggXoL](https://reinsurance.dev/financial-modelling/contracts/aggxol/) (formal) ### AggXoL (Aggregate Excess of Loss) A contract with [attachment](https://reinsurance.dev/glossary/#attachment-point) and [limit](https://reinsurance.dev/glossary/#limit) applied to the total annual (aggregate) loss rather than per occurrence. The same operation as an [aggregate stop loss](https://reinsurance.dev/glossary/#aggregate-stop-loss), with one convention between them: a stop loss attaches at a set loss amount or a loss ratio, and is commonly written in loss-ratio terms (attachment and limit as percentages of the subject premium), whereas this site's AggXoL always states both in currency.[^stop-loss-terms] In term notation: $\text{agg}_{\text{excess}}(A, \ell)$ applied to the trial total. **See also:** [Aggregate Excess](https://reinsurance.dev/glossary/#aggregate-excess), [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss), [Aggregate Stop Loss](https://reinsurance.dev/glossary/#aggregate-stop-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [AggXoL](https://reinsurance.dev/financial-modelling/contracts/aggxol/) (formal) ### Alternative Capital Non-traditional reinsurance capital sourced from capital markets via [ILS](https://reinsurance.dev/glossary/#ils-insurance-linked-securities) structures, [sidecars](https://reinsurance.dev/glossary/#sidecar), or [collateralised reinsurance](https://reinsurance.dev/glossary/#collateralised-reinsurance). About 17% of global reinsurer capital at the end of 2025 (\$136 billion of \$785 billion), sourced on [Market participants](https://reinsurance.dev/foundations/market-participants/#alternative-capital-participants). **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### Attachment Point The loss threshold above which a reinsurance contract begins to pay. In a CatXoL described as "\$30M xs \$20M," the attachment point is \$20M. **See also:** [Limit](https://reinsurance.dev/glossary/#limit), [Retention](https://reinsurance.dev/glossary/#retention) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Attachment Probability The probability that a layer pays: the share of [trials](https://reinsurance.dev/glossary/#trial) in which the loss exceeds the [attachment point](https://reinsurance.dev/glossary/#attachment-point), on the basis the layer attaches on. Aggregate basis, on trial totals: $P_{\text{attach}} = \frac{1}{N} \sum_{j=1}^{N} \mathbf{1}[L_j > A]$. Occurrence basis: the same count on each trial's largest occurrence, $\max_{(t,e)} L_{j,t,e} > A$. **This site's convention:** the inequality is strict, because a loss exactly at $A$ recovers nothing; the [EP curve](https://reinsurance.dev/glossary/#ep-curve-exceedance-probability-curve) read at $A$ counts with $\geq$ and gives the share of trials that reached the attachment, which differs wherever trials tie at $A$. **See also:** [Exhaustion Probability](https://reinsurance.dev/glossary/#exhaustion-probability), [Attachment Point](https://reinsurance.dev/glossary/#attachment-point) **Discussed in:** [Attachment and exhaustion probability](https://reinsurance.dev/toolkit/metrics/attachment-and-exhaustion-probability/#attachment-probability) ## B ### Back-Allocation Attributing a loss computed on a group of rows back to the rows of the group. It is needed wherever a non-linear term (an attachment, a limit) acts on a total and the result must still be reported at the finer resolution. The method depends on whether the rows have an order. Rows with a defined claims order are back-allocated by [erosion](https://reinsurance.dev/glossary/#erosion): a trial's occurrences under an aggregate term. Rows with no defined order, such as the geographies and lines of business of one occurrence, are back-allocated in proportion to each row's share of the group's loss, under the occurrence excess and the aggregate excess alike. **Also known as:** disaggregation **See also:** [Erosion](https://reinsurance.dev/glossary/#erosion), [Occurrence Excess](https://reinsurance.dev/glossary/#occurrence-excess), [Aggregate Excess](https://reinsurance.dev/glossary/#aggregate-excess) **Discussed in:** [Aggregate excess](https://reinsurance.dev/financial-modelling/terms/aggregate-excess/) ### Basis Risk The gap between what an index-triggered instrument pays and the buyer's own loss: the payout can arrive when the buyer's loss is small and fail to arrive when it is large. It is the price of a trigger that needs no loss adjustment, as in an [ILW](https://reinsurance.dev/glossary/#ilw-industry-loss-warranty) or a parametric [cat bond](https://reinsurance.dev/glossary/#cat-bond). **See also:** [ILW](https://reinsurance.dev/glossary/#ilw-industry-loss-warranty), [Trigger](https://reinsurance.dev/glossary/#trigger) ### Book (of Business) The set of risks a [cedent](https://reinsurance.dev/glossary/#cedent) has underwritten: the policies whose losses are the [subject loss](https://reinsurance.dev/glossary/#subject-loss) presented to reinsurance. "A hurricane book" or "the Florida book" names a slice of those risks by peril or geography. Distinct from a [portfolio](https://reinsurance.dev/glossary/#portfolio), which is the [reinsurer's](https://reinsurance.dev/glossary/#reinsurer) collection of contracts: a reinsurer's portfolio is assembled from pieces of many cedents' books. **See also:** [Subject Loss](https://reinsurance.dev/glossary/#subject-loss), [Cedent](https://reinsurance.dev/glossary/#cedent), [Portfolio](https://reinsurance.dev/glossary/#portfolio) **Discussed in:** [Risk profiling](https://reinsurance.dev/applications/risk-profiling/) ### Broker An intermediary that connects [cedents](https://reinsurance.dev/glossary/#cedent) with [reinsurers](https://reinsurance.dev/glossary/#reinsurer), structures deals, and facilitates placement. Major broking firms include Aon, Marsh Re (formerly Guy Carpenter), Gallagher Re, and Howden Re. **See also:** [Brokerage](https://reinsurance.dev/glossary/#brokerage), [Placement Slip](https://reinsurance.dev/glossary/#placement-slip), [Submission](https://reinsurance.dev/glossary/#submission) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### Broker Market The reinsurers that write through intermediaries, as against the [direct market](https://reinsurance.dev/glossary/#direct-market), which deals with cedents itself. A cedent reaches the broker market through a [broker](https://reinsurance.dev/glossary/#broker), who carries the [submission](https://reinsurance.dev/glossary/#submission), collects the quotes, and settles the firm order terms. **This site's convention:** *broker market*, where [IRMI](https://www.irmi.com/term/insurance-definitions/brokerage-market) and much of the market say *brokerage market*, because on this site [brokerage](https://reinsurance.dev/glossary/#brokerage) is the fee. **Also known as:** brokerage market **See also:** [Broker](https://reinsurance.dev/glossary/#broker), [Direct Market](https://reinsurance.dev/glossary/#direct-market), [Underwriting Workflow](https://reinsurance.dev/glossary/#underwriting-workflow) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#brokers) ### Brokerage A fixed percentage fee paid to the [broker](https://reinsurance.dev/glossary/#broker) for arranging a reinsurance transaction, typically a small share of premium. **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### Brokerage Market See [Broker Market](https://reinsurance.dev/glossary/#broker-market). ### Burning Cost An experience-rating estimate of a layer's loss cost: the cedent's historical losses to the layer, trended and developed, expressed as a rate on the subject premium; applied to the premium base, the rate yields the loss-cost estimate. Not a synonym for [expected loss (EL)](https://reinsurance.dev/glossary/#el-expected-loss). A burning cost estimates the expected loss cost from the cedent's loss history, whereas EL computes it from the model's trials. Experience rating is outside this site's scope. **Discussed in:** [Expected loss](https://reinsurance.dev/toolkit/metrics/expected-loss/) ## C ### Capital Efficiency The ratio of the capital a set of contracts would require measured standalone to the capital the combined portfolio requires: $\sum_i K_i \,/\, K^{\text{portfolio}}$. The multiplier view of the [diversification benefit](https://reinsurance.dev/glossary/#diversification-benefit): a capital efficiency of $2\times$ means the portfolio requires half the capital the same contracts would standalone, and the difference is capital the portfolio does not have to hold. Caldera Re's figure is worked on the portfolio analytics page. **See also:** [Capital Requirement](https://reinsurance.dev/glossary/#capital-requirement), [Diversification Benefit](https://reinsurance.dev/glossary/#diversification-benefit), [RAROC](https://reinsurance.dev/glossary/#raroc-risk-adjusted-return-on-capital) **Discussed in:** [Portfolio analytics](https://reinsurance.dev/applications/portfolio-analytics/#the-diversification-carried-implicitly) ### Capital Requirement **This site's convention:** the capital a reinsurer holds to support a contract or portfolio is the **unexpected loss**, $K = \text{TVaR}_\alpha - \text{EL}$ at $\alpha = 90\%$ on the demo tier: the amount by which the tail average exceeds the [expected loss](https://reinsurance.dev/glossary/#el-expected-loss) that premium already pays for. It is one economic-capital convention, not a universal definition. Regulatory regimes and firms' internal models set their own risk measure, horizon, and balance-sheet basis. The Solvency II and Swiss Solvency Test calibrations are on [Value at Risk](https://reinsurance.dev/toolkit/metrics/value-at-risk/). **Also known as:** unexpected loss **See also:** [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk), [EL](https://reinsurance.dev/glossary/#el-expected-loss), [Cost of Capital](https://reinsurance.dev/glossary/#cost-of-capital), [Technical Premium](https://reinsurance.dev/glossary/#technical-premium), [Capital Efficiency](https://reinsurance.dev/glossary/#capital-efficiency) **Discussed in:** [Standalone program pricing](https://reinsurance.dev/applications/standalone-pricing/#step-3-from-metrics-to-premium) ### Cat Bond An [insurance-linked security](https://reinsurance.dev/glossary/#ils-insurance-linked-securities) that transfers catastrophe risk to capital market investors. If a defined trigger is met, the cedent receives a payout funded from the collateral and investors lose principal to that extent. Where the payout is proportional, principal falls with the amount by which the underlying loss exceeds the bond's attachment point, so a total loss needs that loss to reach the exhaustion point.[^catbond-payout] **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### Catastrophe A single event or series of related events causing widespread, concentrated losses across many policyholders simultaneously. Catastrophes break the law of large numbers at the insurer level because they generate correlated claims. **Discussed in:** [The market](https://reinsurance.dev/foundations/the-market/) ### Catastrophe Model A software application that models the hazard, vulnerability, and loss characteristics of risks subject to natural or man-made perils. Produces [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) and [ELT](https://reinsurance.dev/glossary/#elt-event-loss-table) data used in all downstream analytics. **See also:** [Vendor Model](https://reinsurance.dev/glossary/#vendor-model), [View of Risk](https://reinsurance.dev/glossary/#view-of-risk) **Discussed in:** [Personas](https://reinsurance.dev/foundations/personas/) ### CatXoL (Catastrophe Excess of Loss) A per-occurrence, non-proportional reinsurance contract with an [attachment point](https://reinsurance.dev/glossary/#attachment-point) and [limit](https://reinsurance.dev/glossary/#limit). The reinsurer pays for individual catastrophe occurrences whose loss falls within the specified layer. In term notation: $\text{CatXoL}(A, \ell, n) = \text{agg}_{\text{excess}}(0,\, (1{+}n) \cdot \ell) \circ \text{occ}_{\text{excess}}(A, \ell)$, the occurrence layer applied to each occurrence independently, capped for the period by an [aggregate limit](https://reinsurance.dev/glossary/#aggregate-limit) that encodes $n$ [reinstatements](https://reinsurance.dev/glossary/#reinstatement) (the scoping [loss filter](https://reinsurance.dev/glossary/#loss-filter) and [contract period](https://reinsurance.dev/glossary/#contract-period) elided). **See also:** [Occurrence Excess](https://reinsurance.dev/glossary/#occurrence-excess), [Aggregate Excess](https://reinsurance.dev/glossary/#aggregate-excess), [Excess of Loss](https://reinsurance.dev/glossary/#excess-of-loss), [AggXoL](https://reinsurance.dev/glossary/#aggxol-aggregate-excess-of-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [CatXoL](https://reinsurance.dev/financial-modelling/contracts/catxol/) (formal) ### Ceded Loss Loss passed from one party to the next under a contract: one party's ceded loss is the next party's [gross loss](https://reinsurance.dev/glossary/#gross-loss) (the same dollars, seen from opposite sides). In the site's dominant usage the [cedent](https://reinsurance.dev/glossary/#cedent) cedes to the [reinsurer](https://reinsurance.dev/glossary/#reinsurer). When a reinsurer cedes outward in turn, the same word names what it transfers through [retrocession](https://reinsurance.dev/glossary/#retrocession), a specific type of [recovery](https://reinsurance.dev/glossary/#recoveries). **See also:** [Gross Loss](https://reinsurance.dev/glossary/#gross-loss), [Recoveries](https://reinsurance.dev/glossary/#recoveries), [Net Loss](https://reinsurance.dev/glossary/#net-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Cedent The insurance company that purchases reinsurance, transferring a portion of its risk to the [reinsurer](https://reinsurance.dev/glossary/#reinsurer). Also called the primary insurer or ceding company. **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### Ceding Commission A commission returned from [reinsurer](https://reinsurance.dev/glossary/#reinsurer) to [cedent](https://reinsurance.dev/glossary/#cedent) to cover the cedent's policy acquisition costs (underwriting expenses, agent commissions), and sometimes part of the reinsurer's margin as well. The commission rate moves with the expected quality of the ceded book, and is written as a flat percentage of ceded premium or as a [sliding scale](https://reinsurance.dev/glossary/#sliding-scale-commission) that varies with the ceded book's loss ratio between a stated minimum and maximum.[^ceding-commission] **See also:** [Profit Commission](https://reinsurance.dev/glossary/#profit-commission), [Sliding Scale Commission](https://reinsurance.dev/glossary/#sliding-scale-commission) ### Cession Percentage The proportion of risk (and premium) transferred from [cedent](https://reinsurance.dev/glossary/#cedent) to [reinsurer](https://reinsurance.dev/glossary/#reinsurer) in a proportional contract such as a [quota share](https://reinsurance.dev/glossary/#quota-share): the parameter $q$ of the $\text{scale}(q)$ term. It is a term of the contract and sits inside its composition, unlike the [participation](https://reinsurance.dev/glossary/#participation), which records the reinsurer's share of the placement and is applied at [roll-up](https://reinsurance.dev/glossary/#roll-up). **See also:** [Quota Share](https://reinsurance.dev/glossary/#quota-share), [Participation](https://reinsurance.dev/glossary/#participation), [Scaling](https://reinsurance.dev/glossary/#scaling) **Discussed in:** [Quota share](https://reinsurance.dev/financial-modelling/contracts/quota-share/), [Scaling](https://reinsurance.dev/financial-modelling/terms/scaling/) ### Co-TVaR (Contribution to TVaR) The average of one loss stream over the trials that form another stream's tail: $\text{Co-TVaR}_\alpha^{S}(X)$ is the mean of $X$ across the worst $k = \lfloor (1-\alpha)\,N \rfloor$ trials of $S$, the same trials that $\text{TVaR}_\alpha(S)$ averages. Because $S$ fixes the tail set, the co-measures of the components of $S$ add exactly to $\text{TVaR}_\alpha(S)$, which is the [Euler allocation](https://reinsurance.dev/glossary/#euler-allocation). With $S$ the portfolio loss and $X$ one contract's participated loss, Co-TVaR is a risk component: that contract's share of a tail the portfolio already holds. [Marginal TVaR](https://reinsurance.dev/glossary/#marginal-tvar) is the risk delta, the change in the tail from adding the contract. **See also:** [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk), [Marginal TVaR](https://reinsurance.dev/glossary/#marginal-tvar), [Euler Allocation](https://reinsurance.dev/glossary/#euler-allocation) **Discussed in:** [Financial perspectives](https://reinsurance.dev/financial-modelling/perspectives/#what-the-split-gives-you), [Portfolio analytics](https://reinsurance.dev/applications/portfolio-analytics/#step-4-slice-the-portfolio) ### Coherent Risk Measure A risk measure $\rho$ that satisfies four axioms: monotonicity (if $X \leq Y$ in every trial, then $\rho(X) \leq \rho(Y)$), [sub-additivity](https://reinsurance.dev/glossary/#sub-additivity) ($\rho(X + Y) \leq \rho(X) + \rho(Y)$), positive homogeneity ($\rho(cX) = c\,\rho(X)$ for $c \geq 0$), and translation invariance ($\rho(X + c) = \rho(X) + c$ for a certain loss $c$). [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) is coherent; [VaR](https://reinsurance.dev/glossary/#var-value-at-risk) satisfies three of the four and fails sub-additivity. **See also:** [Sub-additivity](https://reinsurance.dev/glossary/#sub-additivity), [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk), [VaR](https://reinsurance.dev/glossary/#var-value-at-risk) **Discussed in:** [VaR vs. TVaR](https://reinsurance.dev/toolkit/metrics/var-vs-tvar/) ### Collateralised Reinsurance A reinsurance [contract](https://reinsurance.dev/glossary/#contract) written on ordinary treaty terms but backed by collateral (a trust, a letter of credit, or funds withheld, for the full limit less the net premium) posted usually by an [ILS fund](https://reinsurance.dev/glossary/#ils-fund), rather than by a rated [reinsurer's](https://reinsurance.dev/glossary/#reinsurer) balance sheet. The loss-side analytics are those of the equivalent traditional contract; only the capital behind it differs. **See also:** [Alternative Capital](https://reinsurance.dev/glossary/#alternative-capital), [Fronting](https://reinsurance.dev/glossary/#fronting) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#collateralised-reinsurance) ### Composition A contract's definition as financial terms combined into one transformation; the word names both the act of combining and the result. Written $C = T_k \circ \cdots \circ T_1$ and read right to left: $T_1$ applies first. Compositions connected by [inuring](https://reinsurance.dev/glossary/#inuring) or [forwarding](https://reinsurance.dev/glossary/#forwarding) form a [dependency graph](https://reinsurance.dev/glossary/#dependency-graph), which this site derives from the clauses rather than storing separately. Distinct from a [program](https://reinsurance.dev/glossary/#program), which is the business grouping of contracts. **See also:** [Term](https://reinsurance.dev/glossary/#term-financial-term), [Contract](https://reinsurance.dev/glossary/#contract), [Program](https://reinsurance.dev/glossary/#program) **Discussed in:** [Contracts as compositions](https://reinsurance.dev/financial-modelling/composition/) ### Contract The generic term for any reinsurance agreement, the legal document formalising obligations between a [cedent](https://reinsurance.dev/glossary/#cedent) and one or more [reinsurers](https://reinsurance.dev/glossary/#reinsurer). A contract that covers a defined book of business over a period is called a [treaty](https://reinsurance.dev/glossary/#treaty); one that covers a single risk is called [facultative](https://reinsurance.dev/glossary/#facultative). In the [Financial Modelling](https://reinsurance.dev/financial-modelling/) chapter, a contract is formally modelled as an ordered [composition](https://reinsurance.dev/glossary/#composition) of financial terms applied to input loss data. **See also:** [Treaty](https://reinsurance.dev/glossary/#treaty), [Layer](https://reinsurance.dev/glossary/#layer), [Composition](https://reinsurance.dev/glossary/#composition), [Program](https://reinsurance.dev/glossary/#program) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [Contracts as compositions](https://reinsurance.dev/financial-modelling/composition/) (formal) ### Contract Lifecycle The states of one [contract](https://reinsurance.dev/glossary/#contract) over time: quoted, bound, [in-force](https://reinsurance.dev/glossary/#in-force) from [inception](https://reinsurance.dev/glossary/#inception) to [expiry](https://reinsurance.dev/glossary/#expiry), expired, and in [runoff](https://reinsurance.dev/glossary/#runoff) while claims remain open. It covers the same ground as the later steps of the [underwriting workflow](https://reinsurance.dev/glossary/#underwriting-workflow), seen from the contract instead of from the people working on it. **See also:** [Underwriting Workflow](https://reinsurance.dev/glossary/#underwriting-workflow), [In-force](https://reinsurance.dev/glossary/#in-force), [Renewal Cycle](https://reinsurance.dev/glossary/#renewal-cycle) ### Contract Period The window from a [contract's](https://reinsurance.dev/glossary/#contract) [inception](https://reinsurance.dev/glossary/#inception) to its [expiry](https://reinsurance.dev/glossary/#expiry), and the financial term that enforces it: a date-range check that keeps only the [occurrences](https://reinsurance.dev/glossary/#occurrence) whose timestamp falls inside the window, on a [losses-occurring](https://reinsurance.dev/glossary/#losses-occurring) basis. Notation $\text{period}(t_0, t_1)$. This is the one name the site uses for the term; "coverage period" and "time filter" are not used. **See also:** [Inception](https://reinsurance.dev/glossary/#inception), [Expiry](https://reinsurance.dev/glossary/#expiry), [Losses Occurring](https://reinsurance.dev/glossary/#losses-occurring), [Term](https://reinsurance.dev/glossary/#term-financial-term) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ### Cost of Capital The required return on capital committed by shareholders to support risk-taking. AM Best's estimates of reinsurers' cost of equity run from 7.5% (CAPM) to 16.0% (market-derived capital pricing model); this site's examples use 10%, inside that range (sourced on [Standalone program pricing](https://reinsurance.dev/applications/standalone-pricing/)). Used to compute the capital charge component of the [technical premium](https://reinsurance.dev/glossary/#technical-premium): Capital Cost = [Capital Requirement](https://reinsurance.dev/glossary/#capital-requirement) × Cost of Capital Rate. **See also:** [Capital Requirement](https://reinsurance.dev/glossary/#capital-requirement), [Technical Premium](https://reinsurance.dev/glossary/#technical-premium), [RAROC](https://reinsurance.dev/glossary/#raroc-risk-adjusted-return-on-capital) **Discussed in:** [Standalone program pricing](https://reinsurance.dev/applications/standalone-pricing/) ### Covered Loss The covered, in-period slice of the [subject loss](https://reinsurance.dev/glossary/#subject-loss): what remains after a [contract](https://reinsurance.dev/glossary/#contract)'s [filter](https://reinsurance.dev/glossary/#loss-filter) and [contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) select the losses the contract responds to, before the transforming terms (attachment, limit, cession) apply. Written $L_j^{\text{cov}}$. Whenever the filter is not the identity, the covered loss and the subject loss are different numbers. Conflating them mislabels real dollars. **See also:** [Subject Loss](https://reinsurance.dev/glossary/#subject-loss), [Gross Loss](https://reinsurance.dev/glossary/#gross-loss), [Filter](https://reinsurance.dev/glossary/#loss-filter) **Discussed in:** [Financial perspectives](https://reinsurance.dev/financial-modelling/perspectives/) ### CTE (Conditional Tail Expectation) The expected loss conditional on the loss being at or above the [VaR](https://reinsurance.dev/glossary/#var-value-at-risk) threshold. Coincides with [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) and [Expected Shortfall (ES)](https://reinsurance.dev/glossary/#es-expected-shortfall) for continuous distributions; on a discrete trial set, conditioning on the loss value includes every trial tied at the threshold and can fail [sub-additivity](https://reinsurance.dev/glossary/#sub-additivity). Where this site uses the name, it computes the rank-based [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk); Metrics compares this divergence with ES's. **Discussed in:** [Tail Value at Risk](https://reinsurance.dev/toolkit/metrics/tail-value-at-risk/) ## D ### Damage Ratio Modelled loss expressed as a fraction of the [total insured value](https://reinsurance.dev/glossary/#tiv-total-insured-value) the events touched: $\text{DR}(S) = \sum_{r \in S} \text{loss}_r / \sum_{r \in S} \text{tiv}_r$ over a set of [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) rows $S$. A damage ratio of 12% means the modelled events destroyed, on average, 12% of the insured value in their path. Computed per occurrence or aggregated per slice (peril, geography, line of business); homogeneous slice-level damage ratios are a basic data-quality signal in [post-model reporting](https://reinsurance.dev/glossary/#post-model-report). **See also:** [TIV](https://reinsurance.dev/glossary/#tiv-total-insured-value), [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#tiv-and-the-damage-ratio), [Risk profiling](https://reinsurance.dev/applications/risk-profiling/) ### Demo Tier This site's 20-[trial](https://reinsurance.dev/glossary/#trial) dataset, sized so every worked example on the site can be checked by hand. A 1,000-trial tier drawn from the same simulation is published alongside it for contrast. Demo-scale losses are far more frequent and severe relative to the contract limits than any real book, so every premium-derived ratio computed on it ([rate on line](https://reinsurance.dev/glossary/#rate-on-line-rol), [loss ratio](https://reinsurance.dev/glossary/#loss-ratio), [RAROC](https://reinsurance.dev/glossary/#raroc-risk-adjusted-return-on-capital)) demonstrates method rather than a market benchmark. **See also:** [Trial](https://reinsurance.dev/glossary/#trial), [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#demo-scale) ### Dependency Graph The directed graph that emerges from tracing data dependencies between [contract](https://reinsurance.dev/glossary/#contract) [compositions](https://reinsurance.dev/glossary/#composition), when one contract's output is the input to another (via [inuring](https://reinsurance.dev/glossary/#inuring) or [forwarding](https://reinsurance.dev/glossary/#forwarding)). This site derives the graph by tracing dependencies rather than storing it: contracts are written as compositions, and the graph follows from how they connect. **Discussed in:** [Programs](https://reinsurance.dev/financial-modelling/programs/) ### Direct Market The reinsurers that deal with cedents themselves rather than through an intermediary, as against the [broker market](https://reinsurance.dev/glossary/#broker-market), where a [broker](https://reinsurance.dev/glossary/#broker) carries the [submission](https://reinsurance.dev/glossary/#submission), collects the quotes, and settles the firm order terms. **See also:** [Broker](https://reinsurance.dev/glossary/#broker), [Brokerage](https://reinsurance.dev/glossary/#brokerage), [Underwriting Workflow](https://reinsurance.dev/glossary/#underwriting-workflow) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### Disaggregation Another name for [back-allocation](https://reinsurance.dev/glossary/#back-allocation). ### Diversification Benefit The reduction in portfolio risk that comes from combining uncorrelated or weakly correlated exposures. Measured on capital it is $\text{DB} = \sum_i K_i - K^{\text{portfolio}}$, where $K_i$ is contract $i$'s [capital requirement](https://reinsurance.dev/glossary/#capital-requirement) measured standalone. A well-diversified portfolio requires less capital than the sum of its parts, sourced on [Personas](https://reinsurance.dev/foundations/personas/#the-chief-underwriting-officer-cuo). **Discussed in:** [Portfolios](https://reinsurance.dev/financial-modelling/portfolios/#expected-loss-adds-tail-risk-diversifies), [Portfolio analytics](https://reinsurance.dev/applications/portfolio-analytics/#the-diversification-carried-implicitly) ### Double Recovery The same dollar of loss recovered under two contracts. Within a [program](https://reinsurance.dev/glossary/#program) it is prevented by [inuring](https://reinsurance.dev/glossary/#inuring): the lower contracts' recoveries are taken out of the beneficiary contract's subject loss before its terms run. An evaluation that ignores the inuring order overstates the beneficiary's gross loss by exactly the doubly recovered amount. **See also:** [Inuring](https://reinsurance.dev/glossary/#inuring), [Program](https://reinsurance.dev/glossary/#program) **Discussed in:** [Programs](https://reinsurance.dev/financial-modelling/programs/#inuring) ## E ### EL (Expected Loss) The average loss across all trials, the most basic risk metric: $\text{EL} = \frac{1}{N}\sum_{j=1}^{N} L_j$. Distinct from the [burning cost](https://reinsurance.dev/glossary/#burning-cost), which estimates the same quantity from the cedent's historical experience instead of from the model's trials. **Also known as:** average annual loss (AAL), in vendor language **See also:** [Burning Cost](https://reinsurance.dev/glossary/#burning-cost), [Technical Premium](https://reinsurance.dev/glossary/#technical-premium), [Loss Ratio](https://reinsurance.dev/glossary/#loss-ratio) **Discussed in:** [Expected loss](https://reinsurance.dev/toolkit/metrics/expected-loss/) ### ELT (Event Loss Table) A table of event-level losses without trial context, with core columns `(event_id, rate, loss)`, where `rate` is the event's annual frequency; vendor schemas add columns (loss standard deviations for [secondary uncertainty](https://reinsurance.dev/glossary/#secondary-uncertainty), exposure values) and naming varies. Unlike a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), events in an ELT are independent and carry a rate rather than being grouped into trials, so the ELT preserves no co-occurrence or temporal sequencing. Converting an ELT to a YELT means simulating trials; collapsing a YELT to an ELT is lossy. **See also:** [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [Event](https://reinsurance.dev/glossary/#event) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#event-loss-tables) ### EP Curve (Exceedance Probability Curve) A curve showing the probability that losses exceed each possible threshold. The fundamental visualisation of catastrophe risk. Comes in two forms: [OEP](https://reinsurance.dev/glossary/#oep-occurrence-exceedance-probability) and [AEP](https://reinsurance.dev/glossary/#aep-aggregate-exceedance-probability). **Discussed in:** [Exceedance probability curves](https://reinsurance.dev/toolkit/distributions/#what-an-ep-curve-represents) ### Erosion The progressive consumption of an aggregate [layer](https://reinsurance.dev/glossary/#layer) as a [trial's](https://reinsurance.dev/glossary/#trial) [occurrences](https://reinsurance.dev/glossary/#occurrence) accumulate against its [attachment](https://reinsurance.dev/glossary/#attachment-point) and [limit](https://reinsurance.dev/glossary/#limit), taken in claims order (chronological within the trial). Each occurrence's erosion is the increase in the layered running aggregate it causes, so the contributions sum to the trial total exactly, and attributing an [aggregate excess](https://reinsurance.dev/glossary/#aggregate-excess)'s gross loss by erosion keeps its output a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table). Erosion is [back-allocation](https://reinsurance.dev/glossary/#back-allocation) for rows that have an order; a proportional attribution across the trial's occurrences is the recognised variant, with the same trial total. **See also:** [Aggregate Excess](https://reinsurance.dev/glossary/#aggregate-excess), [Back-Allocation](https://reinsurance.dev/glossary/#back-allocation), [Aggregate Deductible](https://reinsurance.dev/glossary/#aggregate-deductible), [Layer](https://reinsurance.dev/glossary/#layer) **Discussed in:** [Aggregate excess](https://reinsurance.dev/financial-modelling/terms/aggregate-excess/) ### ES (Expected Shortfall) The average loss in the worst $(1-\alpha)$ of the distribution. The name used for [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) in banking regulation and the risk-measure literature. Coincides with TVaR and [Conditional Tail Expectation (CTE)](https://reinsurance.dev/glossary/#cte-conditional-tail-expectation) for continuous distributions; on a discrete trial set, the literature's definition splits the boundary trial fractionally, while this site's TVaR averages exactly the worst $k = \lfloor N(1-\alpha) \rfloor$ trials. Metrics compares this divergence with CTE's. **Discussed in:** [Tail Value at Risk](https://reinsurance.dev/toolkit/metrics/tail-value-at-risk/) ### Euler Allocation A method of decomposing a portfolio risk measure (e.g., [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk)) into contributions from individual components, where the contributions sum exactly to the total. Derived from Euler's theorem on homogeneous functions. [Co-TVaR](https://reinsurance.dev/glossary/#co-tvar-contribution-to-tvar) is the Euler allocation of TVaR. ### Event A prototypical physical catastrophe in a model's event catalog, with fixed physical characteristics and a catalog ID (`event_id`): for example, a Category 4 hurricane on a defined track making landfall in Miami. The catalog is shared across [trials](https://reinsurance.dev/glossary/#trial). Each dated appearance of an event inside a trial is an [occurrence](https://reinsurance.dev/glossary/#occurrence), so one event recurs in many trials at different dates. In an [ELT](https://reinsurance.dev/glossary/#elt-event-loss-table) each row is an event; in a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) the `event_id` column references the catalog. **See also:** [Occurrence](https://reinsurance.dev/glossary/#occurrence), [ELT](https://reinsurance.dev/glossary/#elt-event-loss-table) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#events-and-occurrences) ### Event Limit A cap applied to each [occurrence](https://reinsurance.dev/glossary/#occurrence) before any later term acts on it: an [occurrence excess](https://reinsurance.dev/glossary/#occurrence-excess) with zero attachment. Used on [quota share](https://reinsurance.dev/glossary/#quota-share) contracts, where it caps each occurrence before the [cession percentage](https://reinsurance.dev/glossary/#cession-percentage) applies and leaves the reinsurer's per-event exposure at $q \cdot \ell_e$. **This site's convention:** the cap sits on the subject occurrence; filed wordings place it on the reinsurer's share, and a ceded-side limit $\ell$ is the subject-side limit $\ell / q$. Contrast the [aggregate limit](https://reinsurance.dev/glossary/#aggregate-limit), which caps the period total. **See also:** [Aggregate Limit](https://reinsurance.dev/glossary/#aggregate-limit), [Limit](https://reinsurance.dev/glossary/#limit), [Quota Share](https://reinsurance.dev/glossary/#quota-share) **Discussed in:** [Quota share](https://reinsurance.dev/financial-modelling/contracts/quota-share/#with-event-limit) ### Excess of Loss A non-proportional reinsurance structure where the reinsurer pays losses above an [attachment point](https://reinsurance.dev/glossary/#attachment-point) up to a [limit](https://reinsurance.dev/glossary/#limit). The most common form is the [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss). **See also:** [Quota Share](https://reinsurance.dev/glossary/#quota-share) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Exhaustion Point The top of a layer, $A + \ell$: the loss level at which the [limit](https://reinsurance.dev/glossary/#limit) is fully consumed and the contract pays no more. Losses above it fall back to the [cedent](https://reinsurance.dev/glossary/#cedent), which is why an excess-of-loss [retention](https://reinsurance.dev/glossary/#retention) has two parts: everything below the [attachment point](https://reinsurance.dev/glossary/#attachment-point) and everything above the exhaustion point. **See also:** [Attachment Point](https://reinsurance.dev/glossary/#attachment-point), [Limit](https://reinsurance.dev/glossary/#limit), [Exhaustion Probability](https://reinsurance.dev/glossary/#exhaustion-probability) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/#attachment-and-limit) ### Exhaustion Probability The probability that a layer is fully consumed: the share of [trials](https://reinsurance.dev/glossary/#trial) in which the loss reaches or exceeds the [attachment point](https://reinsurance.dev/glossary/#attachment-point) plus the [limit](https://reinsurance.dev/glossary/#limit), $P_{\text{exhaust}} = \frac{1}{N} \sum_{j=1}^{N} \mathbf{1}[L_j \geq A + \ell]$, on the same basis as the layer's [attachment probability](https://reinsurance.dev/glossary/#attachment-probability). The inequality is $\geq$ where attachment's is strict: a loss exactly at $A + \ell$ pays the full limit. **See also:** [Attachment Probability](https://reinsurance.dev/glossary/#attachment-probability), [Exhaustion Point](https://reinsurance.dev/glossary/#exhaustion-point), [Limit](https://reinsurance.dev/glossary/#limit) **Discussed in:** [Attachment and exhaustion probability](https://reinsurance.dev/toolkit/metrics/attachment-and-exhaustion-probability/#exhaustion-probability) ### Expiry The date on which a reinsurance [contract's](https://reinsurance.dev/glossary/#contract) [contract period](https://reinsurance.dev/glossary/#contract-period) ends. Losses from events after the expiry are not covered by the contract. The contract period runs from [inception](https://reinsurance.dev/glossary/#inception) to expiry. **See also:** [Inception](https://reinsurance.dev/glossary/#inception), [In-force](https://reinsurance.dev/glossary/#in-force) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ### Exposure Management The control of catastrophe risk at the level of a whole [portfolio](https://reinsurance.dev/glossary/#portfolio) rather than of the individual placement: measuring accumulations, tracking them against the risk limits, and reporting the position. It is the function a [portfolio manager](https://reinsurance.dev/glossary/#portfolio-manager) performs, whatever title an organisation gives the role. **See also:** [Portfolio Manager](https://reinsurance.dev/glossary/#portfolio-manager), [Portfolio](https://reinsurance.dev/glossary/#portfolio), [Roll-up](https://reinsurance.dev/glossary/#roll-up) **Discussed in:** [Portfolio analytics](https://reinsurance.dev/applications/portfolio-analytics/#the-business-problem) ## F ### Facultative A reinsurance [contract](https://reinsurance.dev/glossary/#contract) that covers a single, individually underwritten risk, as opposed to a [treaty](https://reinsurance.dev/glossary/#treaty) which covers an entire book of business. Each facultative placement is negotiated separately. This site focuses primarily on treaty reinsurance. **See also:** [Treaty](https://reinsurance.dev/glossary/#treaty), [Contract](https://reinsurance.dev/glossary/#contract) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Financial Modelling The process of applying [contract](https://reinsurance.dev/glossary/#contract) terms to [subject losses](https://reinsurance.dev/glossary/#subject-loss) to produce the reinsurer's [gross loss](https://reinsurance.dev/glossary/#gross-loss). Given subject loss vector $L^{\text{subject}}$ and contract transformation $C$, the gross loss is $L^{\text{gross}} = C(L^{\text{subject}})$. Every contract structure ([quota share](https://reinsurance.dev/glossary/#quota-share), [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss), [AggXoL](https://reinsurance.dev/glossary/#aggxol-aggregate-excess-of-loss)) defines a different transformation. **Discussed in:** [Dissecting a contract](https://reinsurance.dev/financial-modelling/dissection/) ### Forwarding A dependency between reinsurance contracts in which one contract forwards its ceded output to another as that contract's [subject loss](https://reinsurance.dev/glossary/#subject-loss), as an inward contract does to the [retrocession](https://reinsurance.dev/glossary/#retrocession) that protects it. Contrast [inuring](https://reinsurance.dev/glossary/#inuring), where the dependent contract's subject loss is reduced by the other contract's gross loss. Both relationships are edges of the [dependency graph](https://reinsurance.dev/glossary/#dependency-graph). **See also:** [Inuring](https://reinsurance.dev/glossary/#inuring), [Dependency Graph](https://reinsurance.dev/glossary/#dependency-graph), [Retrocession](https://reinsurance.dev/glossary/#retrocession) **Discussed in:** [Programs](https://reinsurance.dev/financial-modelling/programs/#when-layers-reference-one-another) ### Franchise Deductible A deductible structure where, once the loss exceeds the threshold, the entire loss is covered, not only the excess. Contrasts with a standard deductible, which only pays the amount above the threshold. Expressed by a [trigger](https://reinsurance.dev/glossary/#trigger), a term the [contract catalog](https://reinsurance.dev/financial-modelling/contracts/#what-the-catalog-does-not-cover) does not have yet. **See also:** [Trigger](https://reinsurance.dev/glossary/#trigger) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Fronting An arrangement where a licensed insurer issues policies on behalf of an unlicensed reinsurer or [ILS fund](https://reinsurance.dev/glossary/#ils-fund), retaining little or no risk. The fronting company earns a fee for its regulatory licence. **See also:** [Collateralised Reinsurance](https://reinsurance.dev/glossary/#collateralised-reinsurance) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ## G ### Gross Loss From the reinsurer's perspective: the loss the reinsurer assumes after applying [contract](https://reinsurance.dev/glossary/#contract) terms to the [subject loss](https://reinsurance.dev/glossary/#subject-loss). From the cedent's perspective, this same amount is their [ceded loss](https://reinsurance.dev/glossary/#ceded-loss). All loss perspectives on this site default to the reinsurer's point of view unless stated otherwise. **See also:** [Subject Loss](https://reinsurance.dev/glossary/#subject-loss), [Recoveries](https://reinsurance.dev/glossary/#recoveries), [Net Loss](https://reinsurance.dev/glossary/#net-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ## H ### Hard Market A phase of the [market cycle](https://reinsurance.dev/glossary/#market-cycle) characterised by rising prices, restricted capacity, and stricter terms, typically following a major [catastrophe](https://reinsurance.dev/glossary/#catastrophe) that depletes industry capital. **See also:** [Soft Market](https://reinsurance.dev/glossary/#soft-market), [Market Cycle](https://reinsurance.dev/glossary/#market-cycle) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#the-market-cycle) ### Hazard The natural or man-made phenomenon that can cause loss (for example, a hurricane, earthquake, or flood). Used in [catastrophe modelling](https://reinsurance.dev/glossary/#catastrophe-model) to describe the physical event. ### Hours Clause A treaty clause that defines one loss [occurrence](https://reinsurance.dev/glossary/#occurrence) for a catastrophe peril as all loss from that peril within a stated number of consecutive hours (72 hours is a common windstorm window; filed wordings also use 96 and 168, and other perils differ), with the cedent choosing when the window starts. It is the property-cat form of the [occurrence definition](https://reinsurance.dev/glossary/#occurrence-definition), and the mapping from physical events to contractual occurrences that per-occurrence terms depend on. This site assumes the cat model's `event_id` grouping already is that mapping. **See also:** [Occurrence Definition](https://reinsurance.dev/glossary/#occurrence-definition), [Occurrence](https://reinsurance.dev/glossary/#occurrence), [Event](https://reinsurance.dev/glossary/#event) **Discussed in:** [Occurrence excess](https://reinsurance.dev/financial-modelling/terms/occurrence-excess/) ## I ### IBNR (Incurred But Not Reported) Losses that have already happened but have not yet been reported to the insurer, and the reserve held for them. Estimating IBNR is reserving work on past events; this site's analytics concern losses that have not happened yet, and reserving is out of its scope. **Discussed in:** [Scope, conventions & assumptions](https://reinsurance.dev/conventions/) ### ILS (Insurance-Linked Securities) Financial instruments whose value is tied to insurance loss events, allowing capital market investors to take on insurance risk. Includes [cat bonds](https://reinsurance.dev/glossary/#cat-bond), [sidecars](https://reinsurance.dev/glossary/#sidecar), and [collateralised reinsurance](https://reinsurance.dev/glossary/#collateralised-reinsurance). **See also:** [ILS Fund](https://reinsurance.dev/glossary/#ils-fund), [Alternative Capital](https://reinsurance.dev/glossary/#alternative-capital) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### ILS Fund An asset manager that invests in insurance risk on behalf of institutional investors such as pension funds and sovereign wealth funds, through [cat bonds](https://reinsurance.dev/glossary/#cat-bond), [sidecars](https://reinsurance.dev/glossary/#sidecar), and [collateralised reinsurance](https://reinsurance.dev/glossary/#collateralised-reinsurance). It supplies reinsurance capacity without a rated balance sheet, which is why the limit it sells is collateralised. **See also:** [ILS](https://reinsurance.dev/glossary/#ils-insurance-linked-securities), [Alternative Capital](https://reinsurance.dev/glossary/#alternative-capital), [Fronting](https://reinsurance.dev/glossary/#fronting) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#ils-funds) ### ILW (Industry Loss Warranty) A contract that responds when a market-wide industry loss index crosses an agreed threshold, not when the buyer's own losses do. Because the trigger is external, the payout can occur when the buyer's own loss is small and fail to occur when it is large; that gap is [basis risk](https://reinsurance.dev/glossary/#basis-risk). Reinsurers use ILWs as outward protection alongside [retrocession](https://reinsurance.dev/glossary/#retrocession) and [cat bonds](https://reinsurance.dev/glossary/#cat-bond). Its condition is a [trigger](https://reinsurance.dev/glossary/#trigger) evaluated against an external index instead of the contract's own subject loss. **See also:** [Basis Risk](https://reinsurance.dev/glossary/#basis-risk), [Trigger](https://reinsurance.dev/glossary/#trigger), [Recoveries](https://reinsurance.dev/glossary/#recoveries), [Cat Bond](https://reinsurance.dev/glossary/#cat-bond) **Discussed in:** [Financial perspectives](https://reinsurance.dev/financial-modelling/perspectives/#where-the-dollars-go) ### In-force A [contract](https://reinsurance.dev/glossary/#contract) that is currently within its [contract period](https://reinsurance.dev/glossary/#contract-period) (from the contract perspective) or that has outstanding obligations (from the reinsurer perspective). The two meanings can diverge: a contract may be past its [expiry](https://reinsurance.dev/glossary/#expiry) date but still in-force from the reinsurer's perspective if it has outstanding claims, as [long-tail](https://reinsurance.dev/glossary/#long-tail) business does for years. **See also:** [Inception](https://reinsurance.dev/glossary/#inception), [Expiry](https://reinsurance.dev/glossary/#expiry), [Runoff](https://reinsurance.dev/glossary/#runoff), [Contract Lifecycle](https://reinsurance.dev/glossary/#contract-lifecycle) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ### Inception The date on which a reinsurance [contract's](https://reinsurance.dev/glossary/#contract) [contract period](https://reinsurance.dev/glossary/#contract-period) begins. Losses from events before inception are not covered. The contract period runs from inception to [expiry](https://reinsurance.dev/glossary/#expiry). **See also:** [Expiry](https://reinsurance.dev/glossary/#expiry), [In-force](https://reinsurance.dev/glossary/#in-force) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ### Inuring A dependency between reinsurance contracts in which one contract's gross loss is subtracted from another contract's [subject loss](https://reinsurance.dev/glossary/#subject-loss) before that contract's terms run: `subject_net_of_inuring = subject - gross_of_inuring_contract`. The verb takes the lower contract as its subject: C1 and C2 inure to the benefit of C3, and C3's basis is then net-of-inuring. Contrast [forwarding](https://reinsurance.dev/glossary/#forwarding), where the dependent contract takes the other's ceded output as its input. Both relationships are edges of the [dependency graph](https://reinsurance.dev/glossary/#dependency-graph). **See also:** [Forwarding](https://reinsurance.dev/glossary/#forwarding), [Double Recovery](https://reinsurance.dev/glossary/#double-recovery), [Dependency Graph](https://reinsurance.dev/glossary/#dependency-graph) **Discussed in:** [Programs](https://reinsurance.dev/financial-modelling/programs/#inuring) ## L ### Layer A specific band of coverage within an [excess-of-loss](https://reinsurance.dev/glossary/#excess-of-loss) structure, defined by its [attachment point](https://reinsurance.dev/glossary/#attachment-point) and [limit](https://reinsurance.dev/glossary/#limit). A [contract](https://reinsurance.dev/glossary/#contract) described as "\$30M xs \$20M" defines a layer from \$20M to \$50M. Multiple layers are typically stacked together within a [program](https://reinsurance.dev/glossary/#program). The layer payout function $\min(\max(L - A, 0), \ell)$ is the core of the [occurrence excess](https://reinsurance.dev/financial-modelling/terms/occurrence-excess/) and [aggregate excess](https://reinsurance.dev/financial-modelling/terms/aggregate-excess/) terms. **See also:** [Program](https://reinsurance.dev/glossary/#program), [Attachment Point](https://reinsurance.dev/glossary/#attachment-point), [Limit](https://reinsurance.dev/glossary/#limit) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [Occurrence excess](https://reinsurance.dev/financial-modelling/terms/occurrence-excess/) (formal) ### Limit The maximum amount a reinsurance contract will pay for a covered event or period. In a CatXoL described as "\$30M xs \$20M," the limit is \$30M. **See also:** [Attachment Point](https://reinsurance.dev/glossary/#attachment-point) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Line of Business (LOB) The product or coverage class a policy belongs to: residential property, commercial property, and so on. In this site's [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) schema it is a column, and one of the dimensions a [filter](https://reinsurance.dev/glossary/#loss-filter) can scope a contract to. A single [occurrence](https://reinsurance.dev/glossary/#occurrence) commonly spans several lines of business, which is why occurrence-level terms group their rows before they act. **See also:** [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [Filter](https://reinsurance.dev/glossary/#loss-filter), [Book (of Business)](https://reinsurance.dev/glossary/#book-of-business) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#the-yelt) ### Long-Tail Business whose claims are reported and settled over many years after the contract period ends: liability and other casualty lines. A long-tail contract stays [in-force](https://reinsurance.dev/glossary/#in-force) from the reinsurer's perspective long after [expiry](https://reinsurance.dev/glossary/#expiry). Out of scope for this site, which treats [short-tail](https://reinsurance.dev/glossary/#short-tail) property catastrophe business. **See also:** [Short-Tail](https://reinsurance.dev/glossary/#short-tail), [Runoff](https://reinsurance.dev/glossary/#runoff), [IBNR](https://reinsurance.dev/glossary/#ibnr-incurred-but-not-reported) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ### Loss Corridor A loss-sensitive feature of a proportional contract: a band (customarily of [loss ratio](https://reinsurance.dev/glossary/#loss-ratio), sometimes of currency) within which the [cedent](https://reinsurance.dev/glossary/#cedent) takes losses back. Below the band the reinsurer pays its share, inside it the cedent bears the losses in full or in an agreed proportion, and above it the reinsurer's share resumes. Not a gap between excess-of-loss layers. Because the corridor is defined on the period's aggregate, evaluating it needs the running total across occurrences (stateful in the way an [aggregate deductible](https://reinsurance.dev/glossary/#aggregate-deductible) is). **See also:** [Quota Share](https://reinsurance.dev/glossary/#quota-share), [Loss Ratio](https://reinsurance.dev/glossary/#loss-ratio), [Aggregate Deductible](https://reinsurance.dev/glossary/#aggregate-deductible) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Loss Filter A financial term that selects the subset of YELT rows matching specified predicates on categorical columns (peril, geography, line of business). Operates independently on each row. The first term in most [contract](https://reinsurance.dev/glossary/#contract) [compositions](https://reinsurance.dev/glossary/#composition), restricting the scope of downstream transformations. **See also:** [Contract Period](https://reinsurance.dev/glossary/#contract-period), [Term](https://reinsurance.dev/glossary/#term-financial-term) **Discussed in:** [Loss filter](https://reinsurance.dev/financial-modelling/terms/filter/) ### Loss Ratio **This site's convention:** the ratio of modelled [expected loss](https://reinsurance.dev/glossary/#el-expected-loss) to premium, $\text{LR} = \text{EL} / \text{Premium}$, an *ex ante* figure; with paid reinstatements the denominator is premium plus expected [reinstatement premium](https://reinsurance.dev/glossary/#reinstatement-premium). The industry's accounting definition is the realised ratio of incurred loss to earned premium;[^loss-ratio] the modelled form here is its forward-looking analogue, not a substitute. A loss ratio above 100% means the reinsurer expects to lose money on average. **See also:** [EL](https://reinsurance.dev/glossary/#el-expected-loss), [Rate on Line](https://reinsurance.dev/glossary/#rate-on-line-rol), [Technical Premium](https://reinsurance.dev/glossary/#technical-premium) **Discussed in:** [Standalone program pricing](https://reinsurance.dev/applications/standalone-pricing/) ### Loss Set One catastrophe model run's loss output, delivered and validated as a unit: a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) covering one peril or model view for a [submission](https://reinsurance.dev/glossary/#submission), with the label it was delivered under (a title, and the cedent, peril, regions, model and run date it claims). A multi-peril submission arrives as several loss sets (often from different vendor models), which are validated standalone and then reconciled in combination before any analysis is quoted. Loss sets that share trial identity combine by row union into one YELT. Expected loss adds across them; [VaR](https://reinsurance.dev/glossary/#var-value-at-risk) and [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) in general do not. **See also:** [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [Submission](https://reinsurance.dev/glossary/#submission), [Catastrophe Model](https://reinsurance.dev/glossary/#catastrophe-model) **Discussed in:** [Risk profiling](https://reinsurance.dev/applications/risk-profiling/) ### Losses Occurring The coverage basis on which a contract responds to losses by the **date of the event**: an [occurrence](https://reinsurance.dev/glossary/#occurrence) is covered when it falls between [inception](https://reinsurance.dev/glossary/#inception) and [expiry](https://reinsurance.dev/glossary/#expiry), whichever policy it arose under. The basis this site assumes throughout and the one its [contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) term implements: the only one a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) can express, since it needs no more than the occurrence timestamp. The contrasting bases are [risks attaching](https://reinsurance.dev/glossary/#risks-attaching) and [underwriting year](https://reinsurance.dev/glossary/#underwriting-year); both need each loss's original policy inception date, which a YELT row does not carry. **See also:** [Risks Attaching](https://reinsurance.dev/glossary/#risks-attaching), [Underwriting Year](https://reinsurance.dev/glossary/#underwriting-year), [Inception](https://reinsurance.dev/glossary/#inception), [Expiry](https://reinsurance.dev/glossary/#expiry) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ## M ### Marginal Impact The change in a portfolio-level metric caused by adding or removing one contract. Measured on [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) it is the [Marginal TVaR](https://reinsurance.dev/glossary/#marginal-tvar); measured on the [capital requirement](https://reinsurance.dev/glossary/#capital-requirement) it is the $\Delta K$ of [marginal pricing](https://reinsurance.dev/glossary/#marginal-pricing), $\Delta K = K^{\text{portfolio}+X} - K^{\text{portfolio}}$: the capital requirement of the portfolio with the contract's participated loss $X$ added, minus the capital requirement of the portfolio without it. **See also:** [Marginal TVaR](https://reinsurance.dev/glossary/#marginal-tvar), [Marginal Pricing](https://reinsurance.dev/glossary/#marginal-pricing) ### Marginal Pricing A pricing approach that computes the [technical premium](https://reinsurance.dev/glossary/#technical-premium) using the marginal capital impact ($\Delta K$) rather than the standalone capital requirement. The marginal technical premium is: $\text{EL} + \text{Expenses} + \Delta K \times r_c$. When a contract diversifies the portfolio, the marginal premium is lower than the standalone premium. When it concentrates risk, they converge. **See also:** [Marginal TVaR](https://reinsurance.dev/glossary/#marginal-tvar), [Marginal Impact](https://reinsurance.dev/glossary/#marginal-impact), [Technical Premium](https://reinsurance.dev/glossary/#technical-premium) ### Marginal TVaR The change in a portfolio's [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) from adding one contract: $\Delta\text{TVaR}_\alpha(X) = \text{TVaR}_\alpha(L^{\text{portfolio}} + X) - \text{TVaR}_\alpha(L^{\text{portfolio}})$, where $X$ is the contract's participated loss per trial. It is a risk delta, the [marginal impact](https://reinsurance.dev/glossary/#marginal-impact) measured on TVaR, and the decision to add the contract depends on it.[^marginal-senses] [Co-TVaR](https://reinsurance.dev/glossary/#co-tvar-contribution-to-tvar) is a risk component: the contract's share of a tail the portfolio already holds. The components of a portfolio add to its TVaR; the deltas of its contracts do not. **See also:** [Co-TVaR](https://reinsurance.dev/glossary/#co-tvar-contribution-to-tvar), [Marginal Impact](https://reinsurance.dev/glossary/#marginal-impact), [Marginal Pricing](https://reinsurance.dev/glossary/#marginal-pricing) **Discussed in:** [Additional metrics](https://reinsurance.dev/toolkit/metrics/additional-metrics/#portfolio-level-metrics) ### Market Cycle The alternation of the reinsurance market between [hard](https://reinsurance.dev/glossary/#hard-market) and [soft](https://reinsurance.dev/glossary/#soft-market) phases, driven by catastrophe losses, capital flows, and competition. Its period is irregular. Not the [renewal cycle](https://reinsurance.dev/glossary/#renewal-cycle), the annual calendar on which contracts come up for renewal. **Also known as:** underwriting cycle, the insurance-economics literature's name for it **See also:** [Hard Market](https://reinsurance.dev/glossary/#hard-market), [Soft Market](https://reinsurance.dev/glossary/#soft-market), [Renewal Cycle](https://reinsurance.dev/glossary/#renewal-cycle) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#the-market-cycle) ### Monte Carlo Simulation A method of estimating probability distributions by repeated random sampling. In catastrophe modelling, Monte Carlo simulation samples from event catalogs to generate thousands of [trials](https://reinsurance.dev/glossary/#trial), synthetic futures that form the basis for all downstream analytics. The output is a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table). **See also:** [Trial](https://reinsurance.dev/glossary/#trial), [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [Catastrophe Model](https://reinsurance.dev/glossary/#catastrophe-model) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/) ## N ### Net Loss [Gross loss](https://reinsurance.dev/glossary/#gross-loss) minus [recoveries](https://reinsurance.dev/glossary/#recoveries): what actually stays on the reinsurer's books after all outward protections. Market usage sometimes calls this the reinsurer's "retained loss"; this site reserves *retained* for the cedent's side (see [Retained Loss](https://reinsurance.dev/glossary/#retained-loss)). **See also:** [Gross Loss](https://reinsurance.dev/glossary/#gross-loss), [Recoveries](https://reinsurance.dev/glossary/#recoveries), [Retained Loss](https://reinsurance.dev/glossary/#retained-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### No Claims Bonus A premium adjustment that returns a portion of premium to the [cedent](https://reinsurance.dev/glossary/#cedent) if losses remain below a defined threshold during the contract period. **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Non-Proportional Reinsurance A reinsurance structure where the reinsurer pays only when losses exceed a threshold. Includes [excess of loss](https://reinsurance.dev/glossary/#excess-of-loss), [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss), and [aggregate stop loss](https://reinsurance.dev/glossary/#aggregate-stop-loss) contracts. **See also:** [Proportional Reinsurance](https://reinsurance.dev/glossary/#proportional-reinsurance) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Nth-Event Cover A catastrophe excess-of-loss contract meant to respond only from the second (or a later) [occurrence](https://reinsurance.dev/glossary/#occurrence) of the [contract period](https://reinsurance.dev/glossary/#contract-period) onward: a second-event cover leaves the first occurrence with the cedent. Wordings take two forms. Some are written in dollars: the layer's excess losses carry an aggregate retention of one occurrence limit for each occurrence the cover excludes, which the existing [occurrence excess](https://reinsurance.dev/glossary/#occurrence-excess) and [aggregate excess](https://reinsurance.dev/glossary/#aggregate-excess) express; a second-event cover with no reinstatement is $\text{agg}_{\text{excess}}(\ell, \ell) \circ \text{occ}_{\text{excess}}(A, \ell)$ (the scoping [loss filter](https://reinsurance.dev/glossary/#loss-filter) and [contract period](https://reinsurance.dev/glossary/#contract-period) elided).[^second-event] The dollar form approximates the count rather than reproducing it: a first occurrence that uses only part of the layer leaves the rest of the aggregate retention for the second occurrence to absorb. Wordings that count occurrences order them in [claims order](https://reinsurance.dev/glossary/#erosion): one filed catastrophe contract's first-event coverage responds to "the first Loss Occurrence, chronologically". No current financial term counts occurrences, so the count-based form is outside the [contract catalog](https://reinsurance.dev/financial-modelling/contracts/#what-the-catalog-does-not-cover). **See also:** [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss), [Aggregate Excess](https://reinsurance.dev/glossary/#aggregate-excess), [Occurrence Excess](https://reinsurance.dev/glossary/#occurrence-excess), [Occurrence](https://reinsurance.dev/glossary/#occurrence) **Discussed in:** [Contract catalog](https://reinsurance.dev/financial-modelling/contracts/#what-the-catalog-does-not-cover) ## O ### Occurrence A dated instance of a catalog [event](https://reinsurance.dev/glossary/#event) within a [trial](https://reinsurance.dev/glossary/#trial): the realised appearance of an event at a specific time in one simulated future. Identified by the composite key `(trial_id, timestamp, event_id)` in the [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table). An occurrence may span several YELT rows, one for each cedent, geography, and line of business it touched. The event is the reusable prototype; the occurrence is its dated, trial-specific realisation. **See also:** [Event](https://reinsurance.dev/glossary/#event), [Trial](https://reinsurance.dev/glossary/#trial), [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [OEP](https://reinsurance.dev/glossary/#oep-occurrence-exceedance-probability) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#events-and-occurrences) ### Occurrence Definition The treaty wording that says what counts as one loss [occurrence](https://reinsurance.dev/glossary/#occurrence) for per-occurrence terms: for property catastrophe, usually an [hours clause](https://reinsurance.dev/glossary/#hours-clause) per peril, sometimes restricted to a single named event. The per-occurrence formulas on this site take the [YELT's](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) `event_id` as the occurrence and assume the treaty's definition agrees; the definition as a term of its own is out of scope, and a full treatment is *(planned)*. **See also:** [Hours Clause](https://reinsurance.dev/glossary/#hours-clause), [Occurrence](https://reinsurance.dev/glossary/#occurrence), [Event](https://reinsurance.dev/glossary/#event) **Discussed in:** [Occurrence excess](https://reinsurance.dev/financial-modelling/terms/occurrence-excess/) ### Occurrence Excess A financial term that applies an [attachment point](https://reinsurance.dev/glossary/#attachment-point) $A$ and a [limit](https://reinsurance.dev/glossary/#limit) $\ell$ to each [occurrence](https://reinsurance.dev/glossary/#occurrence) independently: $L_{j,t,e}^{\text{gross}} = \min(\max(L_{j,t,e}^{\text{subject}} - A, 0), \ell)$, written $\text{occ}_{\text{excess}}(A, \ell)$. It holds no state across occurrences, and its output keeps the input rows: each occurrence's gross is [back-allocated](https://reinsurance.dev/glossary/#back-allocation) to the occurrence's rows in proportion to their losses. It is the layer of a [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss) and, with zero attachment, a quota share's [event limit](https://reinsurance.dev/glossary/#event-limit). The [aggregate excess](https://reinsurance.dev/glossary/#aggregate-excess) applies the same shape to the trial total instead. **See also:** [Aggregate Excess](https://reinsurance.dev/glossary/#aggregate-excess), [Attachment Point](https://reinsurance.dev/glossary/#attachment-point), [Limit](https://reinsurance.dev/glossary/#limit), [Event Limit](https://reinsurance.dev/glossary/#event-limit), [Term](https://reinsurance.dev/glossary/#term-financial-term) **Discussed in:** [Occurrence excess](https://reinsurance.dev/financial-modelling/terms/occurrence-excess/), [CatXoL](https://reinsurance.dev/financial-modelling/contracts/catxol/) ### OEP (Occurrence Exceedance Probability) EP curve based on the largest single occurrence loss per trial. Contrasts with [AEP](https://reinsurance.dev/glossary/#aep-aggregate-exceedance-probability), which uses total aggregate loss. **Discussed in:** [Exceedance probability curves](https://reinsurance.dev/toolkit/distributions/#oep-vs-aep) ## P ### Participation The percentage share of a [layer](https://reinsurance.dev/glossary/#layer) or [contract](https://reinsurance.dev/glossary/#contract) that one [reinsurer](https://reinsurance.dev/glossary/#reinsurer) takes. A layer is typically placed with several reinsurers (50%, 30%, 20%), each receiving its share of the premium and paying its share of the claims. Participation is not one of the contract's terms: this site [defines every contract at 100%](https://reinsurance.dev/financial-modelling/composition/#composing-contracts-from-the-blocks) and applies the share at [roll-up](https://reinsurance.dev/glossary/#roll-up). Distinct from the [cession percentage](https://reinsurance.dev/glossary/#cession-percentage), which is a term of a proportional contract. **See also:** [Roll-up](https://reinsurance.dev/glossary/#roll-up), [Cession Percentage](https://reinsurance.dev/glossary/#cession-percentage), [Layer](https://reinsurance.dev/glossary/#layer), [Program](https://reinsurance.dev/glossary/#program) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [Portfolios](https://reinsurance.dev/financial-modelling/portfolios/#the-roll-up-participation-then-sum) (formal) ### Per-Risk Excess of Loss An [excess-of-loss](https://reinsurance.dev/glossary/#excess-of-loss) contract whose [attachment point](https://reinsurance.dev/glossary/#attachment-point) and [limit](https://reinsurance.dev/glossary/#limit) apply to each individual risk (a policy or a location) rather than to a catastrophe occurrence. Priced from exposure and loss experience rather than from catastrophe-model output; out of scope for this site, which treats the per-occurrence [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss). **See also:** [Excess of Loss](https://reinsurance.dev/glossary/#excess-of-loss), [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Peril A specific cause of loss such as wind, earthquake, flood, or wildfire. [Catastrophe models](https://reinsurance.dev/glossary/#catastrophe-model) are typically organised by peril, and this site's [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) schema carries it as the `peril` column (HU, EQ, WS). ### Placement Slip The broker's document that states the terms of a placement (the business covered, the period, attachment, limit, premium, and each reinsurer's [participation](https://reinsurance.dev/glossary/#participation)) and that the participating reinsurers sign. It is written in business language, so encoding it as a [composition](https://reinsurance.dev/glossary/#composition) of terms is an act of interpretation. **Also known as:** slip (trade jargon) **See also:** [Broker](https://reinsurance.dev/glossary/#broker), [Underwriting Workflow](https://reinsurance.dev/glossary/#underwriting-workflow) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#brokers) ### PLT (Period Loss Table) Moody's RMS's name for the [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table). ### PML (Probable Maximum Loss) An estimate of the largest loss a portfolio or risk is expected to sustain from a single [occurrence](https://reinsurance.dev/glossary/#occurrence), typically at a specified [return period](https://reinsurance.dev/glossary/#return-period) (e.g., the 1-in-250 year PML). Used by [reinsurers](https://reinsurance.dev/glossary/#reinsurer), rating agencies, and regulators to set risk limits and assess capital adequacy. **See also:** [OEP](https://reinsurance.dev/glossary/#oep-occurrence-exceedance-probability), [VaR](https://reinsurance.dev/glossary/#var-value-at-risk), [Capital Requirement](https://reinsurance.dev/glossary/#capital-requirement) **Discussed in:** [Personas](https://reinsurance.dev/foundations/personas/) ### Portfolio A collection of reinsurance [contracts](https://reinsurance.dev/glossary/#contract) held by a reinsurer. Portfolio-level analytics (diversification, marginal impact, capital allocation) are a core concern of this site. **See also:** [Book (of Business)](https://reinsurance.dev/glossary/#book-of-business), [Roll-up](https://reinsurance.dev/glossary/#roll-up), [Portfolio Manager](https://reinsurance.dev/glossary/#portfolio-manager) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [Portfolios](https://reinsurance.dev/financial-modelling/portfolios/) (formal) ### Portfolio Manager The role responsible for the reinsurer's [portfolio](https://reinsurance.dev/glossary/#portfolio) as a whole, not for any one contract: it assesses the portfolio's risk posture, tracks concentrations against the risk limits, and weighs the portfolio's expected loss and capital against the premium it earns. Job titles vary, and this site uses the role name throughout. **See also:** [Portfolio](https://reinsurance.dev/glossary/#portfolio), [Roll-up](https://reinsurance.dev/glossary/#roll-up) **Discussed in:** [Portfolio analytics](https://reinsurance.dev/applications/portfolio-analytics/#the-business-problem) ### Post-Model Report The write-up of catastrophe model output that a [cat modeller](https://reinsurance.dev/foundations/personas/#the-catastrophe-modeller) prepares for an [underwriter](https://reinsurance.dev/foundations/personas/#the-underwriter): a characterisation of a [cedent's](https://reinsurance.dev/glossary/#cedent) exposure and [subject loss](https://reinsurance.dev/glossary/#subject-loss) (loss-set reconciliation, exposure summary, and risk metrics) before any contract is applied. The name varies by organisation (modelling summary, account analytics report); the artifact is universal. **See also:** [Submission](https://reinsurance.dev/glossary/#submission), [Loss Set](https://reinsurance.dev/glossary/#loss-set), [Subject Loss](https://reinsurance.dev/glossary/#subject-loss) **Discussed in:** [Risk profiling](https://reinsurance.dev/applications/risk-profiling/) ### Primary Uncertainty Whether and how often a catalog event occurs; defined with its counterpart under [secondary uncertainty](https://reinsurance.dev/glossary/#secondary-uncertainty). ### Profit Commission A commission paid by the [reinsurer](https://reinsurance.dev/glossary/#reinsurer) to the [cedent](https://reinsurance.dev/glossary/#cedent) as a percentage of the reinsurer's underwriting profit on the contract. Aligns incentives: if the cedent underwrites well, they share in the profit. **See also:** [Ceding Commission](https://reinsurance.dev/glossary/#ceding-commission), [Sliding Scale Commission](https://reinsurance.dev/glossary/#sliding-scale-commission) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Program The structured set of reinsurance protections bought to cover a defined exposure: most often a [cedent](https://reinsurance.dev/glossary/#cedent)'s property-catastrophe book, equally a [reinsurer](https://reinsurance.dev/glossary/#reinsurer)'s own [retrocession](https://reinsurance.dev/glossary/#retrocession) or a single large risk. It typically stacks several excess-of-loss [layers](https://reinsurance.dev/glossary/#layer) into a [tower](https://reinsurance.dev/glossary/#tower), sometimes beside a [quota share](https://reinsurance.dev/glossary/#quota-share). The contracts in a program are each a [composition](https://reinsurance.dev/glossary/#composition), independent of one another in a plain tower and related through [inuring](https://reinsurance.dev/glossary/#inuring) or [forwarding](https://reinsurance.dev/glossary/#forwarding) otherwise. The word is used in this business sense only: the term structure of one contract is a composition, never a program. **See also:** [Tower](https://reinsurance.dev/glossary/#tower), [Layer](https://reinsurance.dev/glossary/#layer), [Contract](https://reinsurance.dev/glossary/#contract), [Composition](https://reinsurance.dev/glossary/#composition), [Retrocession](https://reinsurance.dev/glossary/#retrocession) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [Programs](https://reinsurance.dev/financial-modelling/programs/) (formal) ### Proportional Reinsurance A reinsurance structure where the reinsurer takes a fixed percentage of every loss and receives the same percentage of premium. Includes [quota share](https://reinsurance.dev/glossary/#quota-share) and surplus share contracts. **See also:** [Non-Proportional Reinsurance](https://reinsurance.dev/glossary/#non-proportional-reinsurance) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ## Q ### Quota Share A [proportional reinsurance](https://reinsurance.dev/glossary/#proportional-reinsurance) contract where the reinsurer takes a fixed percentage of every loss (and receives the same percentage of premium). The simplest reinsurance structure. **See also:** [Cession Percentage](https://reinsurance.dev/glossary/#cession-percentage), [Excess of Loss](https://reinsurance.dev/glossary/#excess-of-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) (conceptual), [Quota share](https://reinsurance.dev/financial-modelling/contracts/quota-share/) (formal) ## R ### RAROC (Risk-Adjusted Return on Capital) The expected profit per unit of allocated capital: $\text{RAROC} = (\text{Premium} - \text{EL} - \text{Expenses}) / K$. The primary metric for comparing risk-adjusted profitability across contracts with different risk profiles. With paid reinstatements, premium income includes the expected [reinstatement premium](https://reinsurance.dev/glossary/#reinstatement-premium) and $K$ is measured on the outcome net of it. **See also:** [Capital Requirement](https://reinsurance.dev/glossary/#capital-requirement), [Technical Premium](https://reinsurance.dev/glossary/#technical-premium), [Capital Efficiency](https://reinsurance.dev/glossary/#capital-efficiency) **Discussed in:** [Standalone program pricing](https://reinsurance.dev/applications/standalone-pricing/) ### Rate on Line (ROL) The ratio of premium to [limit](https://reinsurance.dev/glossary/#limit): $\text{ROL} = \text{Premium} / \text{Limit}$. Expresses the cost of coverage as a fraction of the maximum payout. Higher ROL indicates more expensive (typically higher-risk) coverage. **See also:** [Limit](https://reinsurance.dev/glossary/#limit), [Technical Premium](https://reinsurance.dev/glossary/#technical-premium), [Loss Ratio](https://reinsurance.dev/glossary/#loss-ratio) **Discussed in:** [Standalone program pricing](https://reinsurance.dev/applications/standalone-pricing/) ### Recoveries What the reinsurer gets back from its own outward protections. Includes traditional [retrocession](https://reinsurance.dev/glossary/#retrocession) ([ceded loss](https://reinsurance.dev/glossary/#ceded-loss)) as well as parametric instruments such as ILWs and [cat bonds](https://reinsurance.dev/glossary/#cat-bond). [Gross loss](https://reinsurance.dev/glossary/#gross-loss) minus recoveries equals [net loss](https://reinsurance.dev/glossary/#net-loss). Note: from the cedent's perspective, "recoveries" refers to what they receive from the reinsurer, which is the reinsurer's [gross loss](https://reinsurance.dev/glossary/#gross-loss). **See also:** [Gross Loss](https://reinsurance.dev/glossary/#gross-loss), [Net Loss](https://reinsurance.dev/glossary/#net-loss), [Ceded Loss](https://reinsurance.dev/glossary/#ceded-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Reinstatement The restoration of coverage after a loss has eroded the [limit](https://reinsurance.dev/glossary/#limit), typically requiring an additional premium. Introduces intra-trial statefulness into contract evaluation: the response to a subsequent occurrence depends on what prior occurrences consumed. With $n$ reinstatements, the aggregate limit becomes $\text{limit} \times (1 + n)$, a [claims-side encoding](https://reinsurance.dev/financial-modelling/contracts/catxol/#reinstatements-as-the-aggregate-limit) that reproduces the recoveries; the premium side of the provision (free or paid reinstatements, premium pro rata to amount and/or to time) is the [reinstatement premium](https://reinsurance.dev/glossary/#reinstatement-premium). **See also:** [Aggregate Limit](https://reinsurance.dev/glossary/#aggregate-limit), [CatXoL](https://reinsurance.dev/glossary/#catxol-catastrophe-excess-of-loss), [Erosion](https://reinsurance.dev/glossary/#erosion), [Reinstatement Premium](https://reinsurance.dev/glossary/#reinstatement-premium) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/#reinstatements) (conceptual), [CatXoL](https://reinsurance.dev/financial-modelling/contracts/catxol/#reinstatements-as-the-aggregate-limit) (formal) ### Reinstatement Premium The premium the cedent pays for a limit restored by a paid [reinstatement](https://reinsurance.dev/glossary/#reinstatement). It is revenue to the reinsurer, paid in exactly the trials where the layer pays. For $n$ reinstatements at 100%, pro rata to the amount reinstated, the reinstatement premium in trial $j$ is $\mathcal{P} \cdot \min(C(L_j), n\ell) / \ell$, where $\mathcal{P}$ is the layer's premium, $\ell$ its occurrence limit and $C(L_j)$ its ceded loss in the trial. Under a clause that is also pro rata to time, the cedent pays for each reinstatement only for the share of the contract period left on the loss date. The two provisions, amount and time, are independent terms of the clause. Because the premium is received in the loss trials, it reduces the layer's required capital as well as its upfront premium. **See also:** [Reinstatement](https://reinsurance.dev/glossary/#reinstatement), [Technical Premium](https://reinsurance.dev/glossary/#technical-premium) **Discussed in:** [Reinstatement premium](https://reinsurance.dev/financial-modelling/beyond-loss/reinstatement-premium/) (formal), [Standalone program pricing](https://reinsurance.dev/applications/standalone-pricing/#step-4-reinstatement-premium-in-the-price) ### Reinsurance A risk transfer mechanism where an insurance company (the [cedent](https://reinsurance.dev/glossary/#cedent)) purchases coverage from a [reinsurer](https://reinsurance.dev/glossary/#reinsurer), transferring a portion of its exposure to catastrophic or accumulated losses. Enables insurers to write more business, stabilise earnings, and meet regulatory capital requirements. **Discussed in:** [The market](https://reinsurance.dev/foundations/the-market/) ### Reinsurer A company that provides insurance to insurance companies, absorbing a portion of their risk in exchange for premium. **See also:** [Cedent](https://reinsurance.dev/glossary/#cedent), [Retrocession](https://reinsurance.dev/glossary/#retrocession) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### Renewal Cycle The annual repetition of the [underwriting workflow](https://reinsurance.dev/glossary/#underwriting-workflow) for contracts that renew. Most contracts run for twelve months or carry an annual anniversary date, so the same cedents and programs return once a year. Not the [market cycle](https://reinsurance.dev/glossary/#market-cycle), which has no fixed period. **See also:** [Renewal Period](https://reinsurance.dev/glossary/#renewal-period), [Underwriting Workflow](https://reinsurance.dev/glossary/#underwriting-workflow), [Market Cycle](https://reinsurance.dev/glossary/#market-cycle) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#the-market-cycle) ### Renewal Period The weeks before a common [inception](https://reinsurance.dev/glossary/#inception) date in which the contracts incepting on that date are quoted and bound. The principal dates are 1 January (the largest), 1 April, 1 June, and 1 July, sourced on [Market participants](https://reinsurance.dev/foundations/market-participants/#the-market-cycle). **Also known as:** renewal season **See also:** [Renewal Cycle](https://reinsurance.dev/glossary/#renewal-cycle), [Inception](https://reinsurance.dev/glossary/#inception) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#the-market-cycle) ### Retained Loss The cedent-side complement of the ceded loss on a contract: the part of the [subject loss](https://reinsurance.dev/glossary/#subject-loss) the contract did not absorb, $L_j^{\text{ret}} = L_j^{\text{subject}} - L_j^{\text{gross}}$. **This site's convention:** *retained* and *retention* always name the cedent's side, and the reinsurer's position after its own recoveries is the [net loss](https://reinsurance.dev/glossary/#net-loss). The market also calls that position "retained loss". **See also:** [Retention](https://reinsurance.dev/glossary/#retention), [Subject Loss](https://reinsurance.dev/glossary/#subject-loss), [Net Loss](https://reinsurance.dev/glossary/#net-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/#this-sites-convention) (conceptual), [Financial perspectives](https://reinsurance.dev/financial-modelling/perspectives/) (formal) ### Retention The amount of risk or loss that the [cedent](https://reinsurance.dev/glossary/#cedent) keeps rather than transferring to the [reinsurer](https://reinsurance.dev/glossary/#reinsurer). In an [excess of loss](https://reinsurance.dev/glossary/#excess-of-loss) contract, typically the [attachment point](https://reinsurance.dev/glossary/#attachment-point). Like [retained loss](https://reinsurance.dev/glossary/#retained-loss), retention always refers to the cedent's side on this site. **See also:** [Retained Loss](https://reinsurance.dev/glossary/#retained-loss), [Attachment Point](https://reinsurance.dev/glossary/#attachment-point) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Retrocession Reinsurance purchased by a [reinsurer](https://reinsurance.dev/glossary/#reinsurer): "reinsurance of reinsurance." The seller of retrocession is a **retrocessionaire**. **Discussed in:** [The market](https://reinsurance.dev/foundations/the-market/), [Market participants](https://reinsurance.dev/foundations/market-participants/#retrocessionaires) ### Retrocessionaire The seller of [retrocession](https://reinsurance.dev/glossary/#retrocession): a reinsurer's reinsurer. ### Return Period The average interval between losses reaching or exceeding a given amount, the reciprocal of that amount's exceedance probability. The 1-in-200-year loss is the loss amount reached or exceeded with probability $1/200 = 0.5\%$ in any one year: $\text{Return period} = 1/(1 - \alpha)$, so the 1-in-10 loss is $\text{VaR}_{0.90}$. It names a point on the [EP curve](https://reinsurance.dev/glossary/#ep-curve-exceedance-probability-curve), not a schedule: a 1-in-200 loss can occur in two consecutive trials. **See also:** [EP Curve](https://reinsurance.dev/glossary/#ep-curve-exceedance-probability-curve), [VaR](https://reinsurance.dev/glossary/#var-value-at-risk), [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) **Discussed in:** [Metrics](https://reinsurance.dev/toolkit/metrics/#confidence-exceedance-and-return-periods) ### Risks Attaching A coverage basis on which a contract covers the losses of the policies incepting during the contract period, whenever those losses occur. Contrast [losses occurring](https://reinsurance.dev/glossary/#losses-occurring), which covers by event date. It needs each loss's original policy inception date, which a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) row does not carry, so this site's contract period term cannot express it. **See also:** [Losses Occurring](https://reinsurance.dev/glossary/#losses-occurring), [Underwriting Year](https://reinsurance.dev/glossary/#underwriting-year) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ### Roll-up The operation that combines a portfolio's [contracts](https://reinsurance.dev/glossary/#contract) into one loss table: scale each contract's [gross loss](https://reinsurance.dev/glossary/#gross-loss) to the reinsurer's [participation](https://reinsurance.dev/glossary/#participation), then sum across contracts, $L_j^{\text{portfolio}} = \sum_i p_i\,C_i(L_j)$. Summing per trial produces a [YLT](https://reinsurance.dev/glossary/#ylt-year-loss-table), enough for AEP metrics; summing per occurrence produces the portfolio [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), needed for OEP metrics and for occurrence-term [retrocession](https://reinsurance.dev/glossary/#retrocession). The sum is valid only when every contract's YELT comes from one simulation and one trial numbering, so that trial $j$ is the same simulated future in each. A roll-up produces the portfolio's loss table, not the [portfolio](https://reinsurance.dev/glossary/#portfolio). Expected loss adds under it; the portfolio's TVaR is at most the sum of the contracts' participated TVaRs, and the gap is the [diversification benefit](https://reinsurance.dev/glossary/#diversification-benefit), while VaR carries no such guarantee. **See also:** [Participation](https://reinsurance.dev/glossary/#participation), [Portfolio](https://reinsurance.dev/glossary/#portfolio), [YLT](https://reinsurance.dev/glossary/#ylt-year-loss-table), [Diversification Benefit](https://reinsurance.dev/glossary/#diversification-benefit) **Discussed in:** [Portfolios](https://reinsurance.dev/financial-modelling/portfolios/#the-roll-up-participation-then-sum), [Portfolio analytics](https://reinsurance.dev/applications/portfolio-analytics/) ### Runoff Business that is no longer renewed and is left to expire and settle. For one contract it is the time after [expiry](https://reinsurance.dev/glossary/#expiry) while claims are still being settled, short for [short-tail](https://reinsurance.dev/glossary/#short-tail) property catastrophe business and years long for [long-tail](https://reinsurance.dev/glossary/#long-tail) lines. For a portfolio, a runoff view evaluates each contract over the part of its [contract period](https://reinsurance.dev/glossary/#contract-period) that remains at the analysis date, with no renewals assumed, so the exposure declines as contracts expire. **See also:** [In-force](https://reinsurance.dev/glossary/#in-force), [Expiry](https://reinsurance.dev/glossary/#expiry), [Contract Lifecycle](https://reinsurance.dev/glossary/#contract-lifecycle) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ## S ### Scaling A financial term that multiplies every loss value in a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) by a constant factor. Operates independently on each row. The same operation carries two business meanings in two places: a [quota share](https://reinsurance.dev/glossary/#quota-share) cession percentage inside a contract's composition, and the [participation](https://reinsurance.dev/glossary/#participation) share applied at [roll-up](https://reinsurance.dev/glossary/#roll-up). $\text{scale}(0.25)$ transfers 25% of every loss. **See also:** [Cession Percentage](https://reinsurance.dev/glossary/#cession-percentage), [Participation](https://reinsurance.dev/glossary/#participation), [Term](https://reinsurance.dev/glossary/#term-financial-term) **Discussed in:** [Scaling](https://reinsurance.dev/financial-modelling/terms/scaling/) ### Scenario (stress test) A deliberately chosen set of assumptions or parameters used for what-if and stress analysis, for example, "a Category 5 hurricane hits Miami and capital markets fall 30% in the same year." Distinct from a [trial](https://reinsurance.dev/glossary/#trial): a trial is a random draw from the loss model, whereas a scenario is a state of the world specified by hand. This site reserves the word "scenario" for stress testing and what-if analysis; simulated loss data is grouped into [trials](https://reinsurance.dev/glossary/#trial), not scenarios. **See also:** [Trial](https://reinsurance.dev/glossary/#trial) **Discussed in:** [Personas](https://reinsurance.dev/foundations/personas/) ### Secondary Uncertainty The spread of loss given that a catalog [event](https://reinsurance.dev/glossary/#event) occurs: the distribution around the event's mean loss, which a vendor [ELT](https://reinsurance.dev/glossary/#elt-event-loss-table) carries as standard-deviation columns beside the mean. **Primary uncertainty** is whether and how often the event occurs (the `rate`). A production [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) is post-sampling, each occurrence's loss already drawn from that distribution, so the analytics downstream never see the uncertainty columns. The site's demo YELTs give each catalog event one fixed loss. **See also:** [ELT](https://reinsurance.dev/glossary/#elt-event-loss-table), [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [Event](https://reinsurance.dev/glossary/#event) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#event-loss-tables) ### Short-Tail Business whose claims are known and largely settled within months to a few years of the event: property, and property catastrophe in particular. It is why this site can evaluate a contract from the event dates in a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) alone, with no claims-development pattern. Contrast [long-tail](https://reinsurance.dev/glossary/#long-tail). **See also:** [Long-Tail](https://reinsurance.dev/glossary/#long-tail), [Runoff](https://reinsurance.dev/glossary/#runoff) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ### Sidecar A special-purpose vehicle that allows third-party investors to participate in a [reinsurer's](https://reinsurance.dev/glossary/#reinsurer) underwriting results, sharing both premium and losses. **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### Sign Convention The choice of whether losses are stored as positive or negative values. **This site's convention:** loss-positive. `loss` and `tiv` are strictly positive in a base [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), non-negative in a transformed one (a term may output a legitimate zero), and a negative loss anywhere is a validation error. Accounting and finance systems often store losses as negative values, whereas catastrophe-model output stores positive magnitudes. The choice fixes the sort order of the loss distribution and with it which end is the tail, so mixing conventions across data sources produces silently wrong metrics. **See also:** [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [EP Curve](https://reinsurance.dev/glossary/#ep-curve-exceedance-probability-curve), [VaR](https://reinsurance.dev/glossary/#var-value-at-risk) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#sign-convention), [If your losses are negative](https://reinsurance.dev/toolkit/metrics/negative-losses/) ### Signing Down The reduction of every reinsurer's written line so that the [participations](https://reinsurance.dev/glossary/#participation) on an oversubscribed placement add up to the order. The price is unchanged; only the line shrinks. Lines written *to stand* are allocated in full and the rest absorb the cut, so a reinsurer's signed line is partly the broker's and the cedent's decision rather than its own. **See also:** [Participation](https://reinsurance.dev/glossary/#participation), [Broker](https://reinsurance.dev/glossary/#broker), [Underwriting Workflow](https://reinsurance.dev/glossary/#underwriting-workflow) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/#participation) ### Sliding Scale Commission A [ceding commission](https://reinsurance.dev/glossary/#ceding-commission) that adjusts based on the contract's loss experience: the commission rate increases when losses are low and decreases when losses are high, between a stated minimum and maximum. Aligns incentives between [cedent](https://reinsurance.dev/glossary/#cedent) and [reinsurer](https://reinsurance.dev/glossary/#reinsurer). **See also:** [Ceding Commission](https://reinsurance.dev/glossary/#ceding-commission), [Profit Commission](https://reinsurance.dev/glossary/#profit-commission) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Slip Trade jargon for the [placement slip](https://reinsurance.dev/glossary/#placement-slip). ### Soft Market A phase of the [market cycle](https://reinsurance.dev/glossary/#market-cycle) characterised by falling prices, abundant capacity, and looser terms, driven by competition as capital enters the market attracted by prior high returns. **See also:** [Hard Market](https://reinsurance.dev/glossary/#hard-market), [Market Cycle](https://reinsurance.dev/glossary/#market-cycle) **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/#the-market-cycle) ### Standard Deviation A measure of the dispersion of trial losses around the [expected loss](https://reinsurance.dev/glossary/#el-expected-loss). Formally: $\sigma = \sqrt{\frac{1}{N} \sum_{j=1}^{N} (L_j - \text{EL})^2}$, using the population formula ($1/N$): a complete trial set is the probability space, not a sample from one. Appears in simpler pricing models (e.g., the standard deviation loading principle). **See also:** [EL](https://reinsurance.dev/glossary/#el-expected-loss), [VaR](https://reinsurance.dev/glossary/#var-value-at-risk), [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) **Discussed in:** [Additional metrics](https://reinsurance.dev/toolkit/metrics/additional-metrics/#standard-deviation) ### Sub-additivity A property of a risk measure $\rho$ requiring $\rho(X + Y) \leq \rho(X) + \rho(Y)$: the risk of a combined portfolio should not exceed the sum of individual risks. It is one of the four axioms of a [coherent risk measure](https://reinsurance.dev/glossary/#coherent-risk-measure). [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk) always satisfies sub-additivity; [VaR](https://reinsurance.dev/glossary/#var-value-at-risk) does not. **See also:** [Coherent Risk Measure](https://reinsurance.dev/glossary/#coherent-risk-measure), [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk), [VaR](https://reinsurance.dev/glossary/#var-value-at-risk) **Discussed in:** [VaR vs. TVaR](https://reinsurance.dev/toolkit/metrics/var-vs-tvar/#sub-additivity) ### Subject Loss The loss stream entering a [contract](https://reinsurance.dev/glossary/#contract) from the cedent's book: everything the cedent presents, before any term applies. The contract's own [filter](https://reinsurance.dev/glossary/#loss-filter) and [contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) select the [covered loss](https://reinsurance.dev/glossary/#covered-loss) from it; the transforming terms ([attachment](https://reinsurance.dev/glossary/#attachment-point), [limit](https://reinsurance.dev/glossary/#limit), [cession rate](https://reinsurance.dev/glossary/#quota-share)) then produce the reinsurer's [gross loss](https://reinsurance.dev/glossary/#gross-loss). Subject and covered loss differ whenever the filter is not the identity: the subject loss is the contract's input, the covered loss the slice it responds to. **See also:** [Covered Loss](https://reinsurance.dev/glossary/#covered-loss), [Gross Loss](https://reinsurance.dev/glossary/#gross-loss), [Net Loss](https://reinsurance.dev/glossary/#net-loss) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Submission The package a [cedent](https://reinsurance.dev/glossary/#cedent) (usually via its [broker](https://reinsurance.dev/glossary/#broker)) sends to reinsurers when seeking coverage: exposure data, historical loss experience, and the desired structure. The submission is the raw input to both catastrophe modelling and underwriting; running it through the models produces the [loss sets](https://reinsurance.dev/glossary/#loss-set) that analytics operates on. **See also:** [Underwriting Workflow](https://reinsurance.dev/glossary/#underwriting-workflow), [Cedent](https://reinsurance.dev/glossary/#cedent), [Broker](https://reinsurance.dev/glossary/#broker), [Loss Set](https://reinsurance.dev/glossary/#loss-set), [Post-Model Report](https://reinsurance.dev/glossary/#post-model-report) **Discussed in:** [Risk profiling](https://reinsurance.dev/applications/risk-profiling/) ### Surplus Share A [proportional reinsurance](https://reinsurance.dev/glossary/#proportional-reinsurance) contract where the cession percentage varies by policy based on the ratio of the sum insured to the cedent's retention line. Policies below the retention are not ceded; policies above are ceded proportionally up to a maximum number of "lines." Modelled as per-policy variable [scaling](https://reinsurance.dev/glossary/#scaling). **See also:** [Quota Share](https://reinsurance.dev/glossary/#quota-share), [Proportional Reinsurance](https://reinsurance.dev/glossary/#proportional-reinsurance) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/#proportional-reinsurance) ## T ### Technical Premium The minimum premium that covers [expected loss](https://reinsurance.dev/glossary/#el-expected-loss), operating expenses, and the [cost of capital](https://reinsurance.dev/glossary/#cost-of-capital): $P = \text{EL} + \text{Expenses} + K \times r_c$. The technical premium is a benchmark: actual market premiums may be higher (hard market) or lower (soft market). With paid reinstatements, the premium and the expected [reinstatement premium](https://reinsurance.dev/glossary/#reinstatement-premium) together cover these costs, and $K$ is measured on the outcome net of the reinstatement premium. **See also:** [EL](https://reinsurance.dev/glossary/#el-expected-loss), [Capital Requirement](https://reinsurance.dev/glossary/#capital-requirement), [Cost of Capital](https://reinsurance.dev/glossary/#cost-of-capital), [Marginal Pricing](https://reinsurance.dev/glossary/#marginal-pricing), [Rate on Line](https://reinsurance.dev/glossary/#rate-on-line-rol) **Discussed in:** [Standalone program pricing](https://reinsurance.dev/applications/standalone-pricing/) ### Term (Financial Term) A self-contained transformation of loss data, the atomic unit of a [contract's](https://reinsurance.dev/glossary/#contract) definition: it takes a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) and produces a YELT, with no side effects and no state carried between trials. State inside a trial is allowed; the [aggregate excess](https://reinsurance.dev/glossary/#aggregate-excess) keeps a running total in claims order. The catalog holds the [loss filter](https://reinsurance.dev/glossary/#loss-filter), [contract period](https://reinsurance.dev/glossary/#contract-period), [scaling](https://reinsurance.dev/glossary/#scaling), [occurrence excess](https://reinsurance.dev/glossary/#occurrence-excess), and [aggregate excess](https://reinsurance.dev/glossary/#aggregate-excess), and terms combine into [compositions](https://reinsurance.dev/glossary/#composition). **Also known as:** building block (informal) **See also:** [Composition](https://reinsurance.dev/glossary/#composition), [Contract](https://reinsurance.dev/glossary/#contract) **Discussed in:** [Contracts as compositions](https://reinsurance.dev/financial-modelling/composition/#the-five-building-blocks) ### TIV (Total Insured Value) The sum of insured values of the exposure a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) row touched, at that row's geography and LOB resolution: the `tiv` column. TIV is the denominator of the [damage ratio](https://reinsurance.dev/glossary/#damage-ratio). The YELT carries only the insured value that modelled events touched (exposed TIV), not the cedent's full book TIV: the complete exposure schedule lives upstream in the catastrophe modelling process. **See also:** [Damage Ratio](https://reinsurance.dev/glossary/#damage-ratio), [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#tiv-and-the-damage-ratio), [Risk profiling](https://reinsurance.dev/applications/risk-profiling/) ### Top & Drop A [program](https://reinsurance.dev/glossary/#program) structure where a single block of limit responds at a higher [layer](https://reinsurance.dev/glossary/#layer) or, when the contract period's first occurrence does not reach that layer, "drops down" and acts as a reinstatement on one or more of the lower layers: flexible coverage from one block of capacity.[^topdrop] It is a relationship between layers, the third besides [inuring](https://reinsurance.dev/glossary/#inuring) and [forwarding](https://reinsurance.dev/glossary/#forwarding): whether the layer drops down depends on the contract period's first occurrence, whether it reached the top layer and how far it eroded the layers below. [Programs](https://reinsurance.dev/financial-modelling/programs/#when-layers-reference-one-another) names it and does not model it. **See also:** [Program](https://reinsurance.dev/glossary/#program), [Inuring](https://reinsurance.dev/glossary/#inuring), [Forwarding](https://reinsurance.dev/glossary/#forwarding), [Layer](https://reinsurance.dev/glossary/#layer) **Discussed in:** [Programs](https://reinsurance.dev/financial-modelling/programs/) ### Tower The stack of excess-of-loss [layers](https://reinsurance.dev/glossary/#layer) placed on one shared exposure, each attaching where the one below exhausts. The ordinary shape of a [program](https://reinsurance.dev/glossary/#program): in a vanilla tower the layers evaluate independently of one another, and only [inuring](https://reinsurance.dev/glossary/#inuring) or [forwarding](https://reinsurance.dev/glossary/#forwarding) makes one layer's result depend on another's. **See also:** [Layer](https://reinsurance.dev/glossary/#layer), [Program](https://reinsurance.dev/glossary/#program), [Inuring](https://reinsurance.dev/glossary/#inuring) **Discussed in:** [Programs](https://reinsurance.dev/financial-modelling/programs/#the-common-shape-a-tower-of-layers) ### Treaty A [contract](https://reinsurance.dev/glossary/#contract) that covers a defined book of business over a set period (usually 12 months, renewing annually), as opposed to [facultative](https://reinsurance.dev/glossary/#facultative) reinsurance which covers individual risks case by case. Most reinsurance placements are treaty-based. Industry practitioners may say "treaty" where this site says "contract." **See also:** [Contract](https://reinsurance.dev/glossary/#contract), [Layer](https://reinsurance.dev/glossary/#layer), [Program](https://reinsurance.dev/glossary/#program) **Discussed in:** [Products and contracts](https://reinsurance.dev/foundations/products-and-contracts/) ### Trial A single simulated draw from the loss model: one possible future over a fixed forward horizon, usually a year but sometimes several (multi-year models support multi-year contracts). Each trial contains zero or more occurrences (each identified by the composite key `(trial_id, timestamp, event_id)`) and is identified by `trial_id` in the [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table). Trials are typically equiprobable, each representing $1/N$ of the simulated probability space. A `trial_id` identifies a trial within one simulation and its trial numbering: trial $j$ is the same simulated future in every YELT from that simulation and numbering, which is what lets losses add per trial across cedents, and equal ids from two simulations (another vendor's model, and usually another model version or climate view) name unrelated trials. The two demo tiers are numbered separately, so Trial 9 of the 20-trial tier is not Trial 9 of the 1,000-trial tier. The word "trial" is reserved for this random-draw unit; a deliberately chosen what-if state is a [scenario](https://reinsurance.dev/glossary/#scenario-stress-test). **See also:** [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [Event](https://reinsurance.dev/glossary/#event), [Occurrence](https://reinsurance.dev/glossary/#occurrence) **Discussed in:** [The trial worldview](https://reinsurance.dev/toolkit/trials/#what-is-a-trial) ### Trigger A financial term that passes the full loss through when a condition is met and returns zero otherwise: a binary gate, all or nothing. The condition is evaluated against a trigger stream that may be the contract's own subject loss ([franchise deductible](https://reinsurance.dev/glossary/#franchise-deductible)) or an external index (industry loss warranty, parametric structures). **See also:** [Franchise Deductible](https://reinsurance.dev/glossary/#franchise-deductible) ### TVaR (Tail Value at Risk) The average loss in the worst trials, at and beyond the [VaR](https://reinsurance.dev/glossary/#var-value-at-risk) threshold: a measure of tail severity, not only of tail probability. Formally $\text{TVaR}_\alpha = \frac{1}{k}\sum_{r=1}^{k} L_{(r)}$, where $L_{(r)}$ is the $r$-th largest trial loss and $k = \lfloor N(1-\alpha) \rfloor$; `NaN` when $k = 0$. Preferred over VaR for capital decisions because it responds to how large the extreme losses are, and because it is a [coherent risk measure](https://reinsurance.dev/glossary/#coherent-risk-measure). **Also known as:** [CTE](https://reinsurance.dev/glossary/#cte-conditional-tail-expectation), [ES](https://reinsurance.dev/glossary/#es-expected-shortfall) (the three coincide for continuous distributions) **See also:** [VaR](https://reinsurance.dev/glossary/#var-value-at-risk), [Co-TVaR](https://reinsurance.dev/glossary/#co-tvar-contribution-to-tvar), [Window TVaR](https://reinsurance.dev/glossary/#window-tvar), [Capital Requirement](https://reinsurance.dev/glossary/#capital-requirement) **Discussed in:** [Tail Value at Risk](https://reinsurance.dev/toolkit/metrics/tail-value-at-risk/) ## U ### Underwriting Cycle The insurance-economics literature's name for the [market cycle](https://reinsurance.dev/glossary/#market-cycle). It does not name the steps a single contract goes through; those are the [underwriting workflow](https://reinsurance.dev/glossary/#underwriting-workflow). ### Underwriting Workflow The sequence of steps a reinsurer takes one contract through: [submission](https://reinsurance.dev/glossary/#submission), modelling, working the deal (structuring and analysis between underwriter, actuary, and cat modeller), quoting, firm order terms (FOT, the final terms the cedent and its broker settle on after collecting quotes), binding, and [expiry](https://reinsurance.dev/glossary/#expiry). For business that renews, it repeats with each [renewal cycle](https://reinsurance.dev/glossary/#renewal-cycle). **See also:** [Contract Lifecycle](https://reinsurance.dev/glossary/#contract-lifecycle), [Renewal Cycle](https://reinsurance.dev/glossary/#renewal-cycle), [Submission](https://reinsurance.dev/glossary/#submission), [Placement Slip](https://reinsurance.dev/glossary/#placement-slip) **Discussed in:** [Personas](https://reinsurance.dev/foundations/personas/#how-the-personas-interact) ### Underwriting Year A coverage and accounting basis that groups losses by the year the underlying policy was written, whenever the loss occurs. Contrast [losses occurring](https://reinsurance.dev/glossary/#losses-occurring). Like [risks attaching](https://reinsurance.dev/glossary/#risks-attaching), it needs a policy inception date a [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) row does not carry. **See also:** [Losses Occurring](https://reinsurance.dev/glossary/#losses-occurring), [Risks Attaching](https://reinsurance.dev/glossary/#risks-attaching) **Discussed in:** [Contract period](https://reinsurance.dev/financial-modelling/terms/contract-period/) ### Unexpected Loss The amount by which a tail loss exceeds the expected loss; on this site, the [capital requirement](https://reinsurance.dev/glossary/#capital-requirement). ## V ### VaR (Value at Risk) The loss threshold at a specified confidence level: a quantile of the loss distribution. Formally $\text{VaR}_\alpha = L_{(k)}$, where $k = \lfloor (1-\alpha) \cdot N \rfloor$ and $L_{(r)}$ is the $r$-th largest trial loss; when $k = 0$ the trial set cannot resolve the level and VaR is `NaN`. **This site's convention:** VaR is always an observed trial loss, never a value interpolated between two ranks as some quantile definitions produce. At the 99% confidence level, VaR is the loss reached or exceeded in 1 out of 100 trials. **See also:** [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk), [EP Curve](https://reinsurance.dev/glossary/#ep-curve-exceedance-probability-curve), [Return Period](https://reinsurance.dev/glossary/#return-period), [Coherent Risk Measure](https://reinsurance.dev/glossary/#coherent-risk-measure) **Discussed in:** [Value at Risk](https://reinsurance.dev/toolkit/metrics/value-at-risk/) ### Vendor Model A [catastrophe model](https://reinsurance.dev/glossary/#catastrophe-model) developed by one of the specialist vendors (Moody's RMS, Verisk, and Cotality, formerly CoreLogic) and offered as a commercial product. **Discussed in:** [Market participants](https://reinsurance.dev/foundations/market-participants/) ### View of Risk A specific perspective on potential losses, shaped by the choice of catastrophe model, assumptions, and parameters used in the analysis. Different views of risk may yield different loss estimates for the same portfolio. ### Vulnerability A measure of how susceptible an exposed asset is to damage from a given [hazard](https://reinsurance.dev/glossary/#hazard). Vulnerability functions translate hazard intensity into expected damage ratios. ## W ### Window TVaR The mean loss within a bounded interval of the EP curve, between two confidence levels $\alpha_{\text{lo}}$ and $\alpha_{\text{hi}}$. Formally: $\text{Window TVaR}(\alpha_{\text{lo}}, \alpha_{\text{hi}}) = \frac{1}{k_{\text{lo}} - k_{\text{hi}}} \sum_{r=k_{\text{hi}}+1}^{k_{\text{lo}}} L_{(r)}$ where $k = \lfloor (1-\alpha) \cdot N \rfloor$. Useful for reporting one band of the tail on its own, differentiating frequency-driven from severity-driven risk, and allocating capital to specific portions of the loss distribution. **See also:** [TVaR](https://reinsurance.dev/glossary/#tvar-tail-value-at-risk), [VaR](https://reinsurance.dev/glossary/#var-value-at-risk), [EP Curve](https://reinsurance.dev/glossary/#ep-curve-exceedance-probability-curve) **Discussed in:** [Additional metrics](https://reinsurance.dev/toolkit/metrics/additional-metrics/#window-tvar) ## Y ### YELT (Year Event Loss Table) The fundamental table of catastrophe risk analytics: one row per [occurrence](https://reinsurance.dev/glossary/#occurrence) loss within a simulated [trial](https://reinsurance.dev/glossary/#trial), for one cedent, geography, and line of business. The industry core is four columns, `(trial_id, timestamp, event_id, loss)`; this site's schema adds five (`peril, geography_id, lob_id, cedent_id, tiv`), an enrichment specific to this site, and vendor and in-house schemas vary in what they carry and what they call it. Despite the name, rows are grouped by trial, not by calendar year (see [the terminology note](https://reinsurance.dev/toolkit/trials/#the-yelt)). `trial_id` identifies a trial within the simulation and trial numbering that produced the YELT, and `event_id` an event within its event catalog, so YELTs join on the occurrence key only when they come from one simulation and numbering. **Also known as:** PLT (period loss table), Moody's RMS's name for the same structure **See also:** [ELT](https://reinsurance.dev/glossary/#elt-event-loss-table), [YLT](https://reinsurance.dev/glossary/#ylt-year-loss-table), [Trial](https://reinsurance.dev/glossary/#trial), [Occurrence](https://reinsurance.dev/glossary/#occurrence), [Sign Convention](https://reinsurance.dev/glossary/#sign-convention) **Discussed in:** [Personas](https://reinsurance.dev/foundations/personas/) (conceptual), [The trial worldview](https://reinsurance.dev/toolkit/trials/#the-yelt) (formal) ### YLT (Year Loss Table) A [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table) reduced to trial resolution: one row per [trial](https://reinsurance.dev/glossary/#trial) with columns `(trial_id, loss)`, the occurrence detail dropped. A trial-level [roll-up](https://reinsurance.dev/glossary/#roll-up) produces a YLT; it supports [AEP](https://reinsurance.dev/glossary/#aep-aggregate-exceedance-probability) metrics but not [OEP](https://reinsurance.dev/glossary/#oep-occurrence-exceedance-probability) metrics or occurrence-term evaluation. The reduction is lossy, irreversible, and always [a chosen one](https://reinsurance.dev/financial-modelling/portfolios/#two-resolutions-trial-and-occurrence): no [financial term](https://reinsurance.dev/glossary/#term-financial-term) outputs a YLT; the [aggregate excess](https://reinsurance.dev/financial-modelling/terms/aggregate-excess/) stays at YELT resolution by [erosion](https://reinsurance.dev/glossary/#erosion) attribution. The "Y" carries the same caveat as the YELT's: rows are trials, not calendar years. **See also:** [YELT](https://reinsurance.dev/glossary/#yelt-year-event-loss-table), [Roll-up](https://reinsurance.dev/glossary/#roll-up), [Trial](https://reinsurance.dev/glossary/#trial) **Discussed in:** [Portfolios](https://reinsurance.dev/financial-modelling/portfolios/) [^stop-loss-terms]: David R. Clark, ["Basics of Reinsurance Pricing"](https://www.casact.org/sites/default/files/old/studynotes_clark_2014.pdf), Casualty Actuarial Society study note, rev. 2014. Describes stop-loss treaties as aggregate covers of losses in excess of a set loss amount or loss ratio. [^ceding-commission]: Guy Carpenter, [Glossary of Reinsurance Terms](https://www.guycarp.com/company/news-and-events/glossary.html), which defines the ceding commission as "an allowance (usually a percentage of the reinsurance premium) made by the reinsurer for part or all of a ceding company's acquisition and other costs" and notes that it "may also include a profit factor for the reinsured", which is where the margin clause above comes from. Swiss Re, [*Proportional and non-proportional reinsurance*](https://newdoc.nccu.edu.tw/teasyllabus/308002308018/Swiss%20Re%20Prop.%26Non-Prop..pdf) (UM3), 1997, §5: whether the commission covers the cedent's expenses "will depend on the quality of the business ceded"; Swiss Re, [*The essential guide to reinsurance*](https://www.swissre.com/dam/jcr:d06472ab-2625-48cf-8b4e-7c7ac8aa63f0/The-essential-guide-to-reinsurance.pdf), p. 25, adds that the commission "is reduced or increased according to the quality of the portfolio". Clark, *Basics of Reinsurance Pricing*, p. 9, works an illustrative sliding scale from a 25% minimum at a 65% loss ratio to a 45% maximum at 35%. No public source states a market-typical range. [^catbond-payout]: Alexander Braun and Carolyn Kousky, [*Catastrophe Bonds*](https://impact.wharton.upenn.edu/wp-content/uploads/2023/08/Cat-Bond-Primer-July-2021.pdf), Wharton Risk Management and Decision Processes Center, July 2021: "Under a proportional payout, the percentage loss of principal suffered by investors rises with the amount by which the underlying insurance losses exceed the attachment point of the catastrophe bond. A full loss for investors is reached once the underlying insurance losses hit the exhaustion point." The primer contrasts this with binary payouts; it does not count how often realised losses have been partial rather than total. [^loss-ratio]: NAIC, [Glossary of Insurance Terms](https://content.naic.org/glossary-insurance-terms), which defines the loss ratio as "the percentage of incurred losses to earned premiums" and, under *Incurred Losses*, those losses as "sustained losses, paid or not, during a specified time period". That practitioners reserve the bare name for the realised figure is this site's assessment, not the NAIC's statement. [^marginal-senses]: Gary G. Venter, John A. Major, and Rodney E. Kreps, ["Marginal Decomposition of Risk Measures"](https://doi.org/10.2143/AST.36.2.2017927), *ASTIN Bulletin* 36(2), 2006: "Marginal impact can be incremental or total, that is the impact could be that of a small change or of the entire business component. Here we adopt the incremental approach." This site takes the total sense for Marginal TVaR; [Co-TVaR](https://reinsurance.dev/glossary/#co-tvar-contribution-to-tvar) is the Euler component the incremental approach yields. John A. Major and Stephen J. Mildenhall, [*Introduction to Capital Modeling and Portfolio Management*](https://www.casact.org/sites/default/files/2026-01/CAS_Monograph_15_-_Intro_to_Capital_Modeling.pdf), CAS Monograph 15, Casualty Actuarial Society, 2026, §3.3, takes the incremental sense as its default, so both meanings of the bare word *marginal* are in use. [^second-event]: United Property & Casualty Insurance Company, ["Second Event Property Catastrophe Excess of Loss Reinsurance Contract"](https://www.sec.gov/Archives/edgar/data/1401521/000140152115000007/exh1082014secondeventcatxo.htm), effective 1 June 2014, filed with the SEC as Exhibit 10.8, 2015. Article 7 caps the reinsurer at \$15,000,000 for any one Loss Occurrence and in all during the term, and provides that "no claim shall be made hereunder unless and until the Company's Subject Excess Losses arising out of Loss Occurrences commencing during the Term exceed \$15,000,000": an aggregate retention of one occurrence limit. Heritage Property & Casualty Insurance Company, ["Second Aggregate Catastrophe Excess of Loss Reinsurance Contract"](https://www.sec.gov/Archives/edgar/data/1598665/000119312514150787/d667216dex104.htm), filed with the SEC as Exhibit 10.4, 2014, whose Coverage A responds "in respect of the first Loss Occurrence, chronologically": the count-based form of the ordering. [^topdrop]: Ivelin Zvezdov, ["Top and Drop: A Reusable and Customizable Reinsurance Solution"](https://www.verisk.com/blog/top-and-drop-a-reusable-and-customizable-reinsurance-solution/), Verisk, September 2016. The clause lets the reinsured reuse "the top excess-of-loss layer in the reinsurance tower if the retention of this top layer is not breached by the first loss event", after which that layer "acts as a reinstatement on one or more of the lower layers".