Glossary

This glossary contains every domain term introduced across the site. Each entry includes a short definition, a formal definition where applicable, and cross-references to the chapters where the term is discussed in depth.

A

AEP (Aggregate Exceedance Probability)

EP curve based on the total (aggregate) loss per scenario across all occurrences in a period. Contrasts with OEP, which uses only the largest single occurrence loss.

Discussed in: Quantification

Aggregate Deductible

The total loss a cedent must absorb across all occurrences in a period before reinsurance responds. Unlike an occurrence-level attachment, an aggregate deductible accumulates losses across occurrences. In operator notation: Threshold(level, {s}, {s,t,e}).

Discussed in: Products and Contracts (conceptual), Quantification (formal)

Aggregate Stop Loss

A reinsurance contract that caps the cedent’s total annual losses above an aggregate deductible. Applies at the scenario (annual) level rather than per occurrence. In operator notation: Cap(limit, {s}, {s,t,e}) ∘ Threshold(A, {s}, {s,t,e}).

Discussed in: Products and Contracts

AggXoL (Aggregate Excess of Loss)

A contract with attachment and limit applied to the total annual (aggregate) loss rather than per occurrence. Structurally identical to an aggregate stop loss — the distinction is a business naming convention. In operator notation: Cap(limit, {s}, {s,t,e}) ∘ Threshold(A, {s}, {s,t,e}).

See also: CatXoL, Aggregate Stop Loss

Discussed in: Products and Contracts, Engineering

Alternative Capital

Non-traditional reinsurance capital sourced from capital markets via ILS structures, sidecars, or collateralized reinsurance. Provides roughly 15-20% of global reinsurance capacity.

Discussed in: 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, Retention

Discussed in: Products and Contracts

Attachment Probability

The probability that a loss exceeds the attachment point of a contract layer. Formally: $P_{\text{attach}} = \frac{1}{N} \sum_{s=1}^{N} \mathbf{1}[L_s > A]$ . A layer with 30% attachment probability means the reinsurer expects to pay a claim roughly 3 years out of 10.

Discussed in: Metrics

B

Back-Allocation

Distributing losses computed at a grouped (aggregate) level back to the original higher-resolution records. Necessary because non-linear operations at a grouped level cannot be applied row by row. The default strategy is proportional allocation based on original loss contribution.

Discussed in: Evaluation Semantics

Broker

An intermediary that connects cedents with reinsurers, structures deals, and facilitates placement. Major broking firms include Aon, Marsh McLennan (Guy Carpenter), and WTW (Willis Re).

Discussed in: Market Participants

Brokerage

A fixed percentage fee paid to the broker for arranging a reinsurance transaction, typically 1–3% of premium.

Discussed in: Expression Composition

Burning Cost

Industry shorthand for expected loss (EL) — the long-run average annual loss. Used informally in pricing discussions.

Discussed in: Metrics

C

Cap

A term operator that limits the grouped loss total to a maximum value. Formally: computes the grouped total, takes the minimum of the total and the cap level, and distributes the result back to individual rows proportionally. Parameterized by a level and a grouping. The complement of Threshold; together they form the Layer function.

See also: Threshold, Layer Function, Limit

Discussed in: Term Algebra

Capital Requirement

The amount of capital a reinsurer must hold to support a contract or portfolio — specifically, the unexpected loss beyond what premium covers. Formally: $K = \text{TVaR}_\alpha - \text{EL}$ . The expected loss is already covered by the premium’s EL component; capital only needs to cover the excess.

Discussed in: Capital and Pricing, Standalone Contract Pricing

Cascading Layers

A reinsurance program structure where multiple layers are stacked on top of each other (“tower” or “step” structure), each operating on the same gross loss independently. Not to be confused with inuring, where layers interact.

See also: Layer

Discussed in: Expression Composition

Cat Bond

An insurance-linked security that transfers catastrophe risk to capital market investors. If a defined trigger is met, investors lose their collateral and the cedent receives a payout.

Discussed in: 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

Catastrophe Model

A software application that models the hazard, vulnerability, and loss characteristics of risks subject to natural or man-made perils. Produces SELT and ELT data used in all downstream analytics.

See also: Vendor Model, View of Risk

Discussed in: Personas

CatXoL (Catastrophe Excess of Loss)

A per-occurrence, non-proportional reinsurance contract with an attachment point and limit. The reinsurer pays for individual catastrophe occurrences whose loss falls within the specified layer. In operator notation: Cap(limit, {s,t,e}, {s,t,e}) ∘ Threshold(A, {s,t,e}, {s,t,e}). The grouping at {s,t,e} (scenario, timestamp, event) makes it occurrence-level.

See also: Excess of Loss, AggXoL

Discussed in: Products and Contracts

Ceded Loss

The portion of loss transferred outward via retrocession or other traditional risk transfer — a specific type of recovery. From the cedent’s perspective, the ceded loss is what flows to the reinsurer (and equals the reinsurer’s gross loss).

See also: Gross Loss, Recoveries, Net Loss

Discussed in: Products and Contracts

Cedent

The insurance company that purchases reinsurance, transferring a portion of its risk to the reinsurer. Also called the primary insurer or ceding company.

Discussed in: Market Participants

Ceding Commission

A commission returned from reinsurer to cedent to cover the cedent’s policy acquisition costs (underwriting expenses, agent commissions). Typically 20–35% of ceded premium.

Discussed in: Expression Composition

Cession Percentage

The proportion of risk (and premium) transferred from cedent to reinsurer in a proportional treaty such as a quota share.

Discussed in: Products and Contracts

Co-TVaR (Contribution to TVaR)

A contract’s contribution to portfolio-level TVaR — a marginal risk metric that captures how much of the portfolio’s tail risk is attributable to a single contract.

Discussed in: Quantification

Contract

The generic term for any reinsurance agreement — the legal document formalizing obligations between a cedent and one or more reinsurers. A contract that covers a defined book of business over a period is called a treaty; one that covers a single risk is called facultative. In the Engineering chapter, a contract is formally modeled as an ordered composition of term operators applied to input loss data.

See also: Treaty, Layer, Program

Discussed in: Products and Contracts (conceptual), Engineering (formal)

CTE (Conditional Tail Expectation)

Synonym for TVaR. The expected loss conditional on being in the worst $(1-\alpha)$ of scenarios. Also called Expected Shortfall (ES).

Discussed in: Metrics

Cost of Capital

The required return on capital committed by shareholders to support risk-taking. Typically 6%–12% in the reinsurance industry. Used to compute the capital charge component of the technical premium: Capital Cost = Capital Requirement × Cost of Capital Rate.

Discussed in: Capital and Pricing

D

Dependency Graph

The directed graph that emerges from tracing data dependencies between contract compositions — when one contract’s output is the input to another (via inuring or sourcing). The engine discovers the graph by tracing dependencies, then uses a topological sort to determine evaluation order.

Discussed in: Expression Composition

Diversification Benefit

The reduction in portfolio risk that comes from combining uncorrelated or weakly correlated exposures. A well-diversified portfolio requires less capital than the sum of its parts.

Discussed in: Quantification

E

EL (Expected Loss)

The average loss across all scenarios — the most basic risk metric. Formally: the arithmetic mean of scenario losses. Also called burning cost.

Discussed in: Metrics

ELT (Event Loss Table)

A table of event-level losses without scenario context. Unlike a SELT, events in an ELT are independent and carry a rate (annual frequency) rather than being grouped into scenarios.

Discussed in: Quantification

ES (Expected Shortfall)

Synonym for TVaR. The expected loss conditional on being in the worst $(1-\alpha)$ of scenarios. Also called Conditional Tail Expectation (CTE).

Discussed in: Metrics

EP Curve (Exceedance Probability Curve)

A curve showing the probability that losses exceed each possible threshold. The fundamental visualization of catastrophe risk. Comes in two forms: OEP and AEP.

Discussed in: Quantification

Euler Allocation

A method of decomposing a portfolio risk measure (e.g., TVaR) into contributions from individual components, where the contributions sum exactly to the total. Derived from Euler’s theorem on homogeneous functions. Co-TVaR is the Euler allocation of TVaR.

Discussed in: Portfolio Aggregation

Evaluation Plan

The engine’s internal execution representation compiled from contract compositions. A topological sort of the dependency graph that determines which contracts can be evaluated in parallel and which must wait for dependencies. One of the four NDA-safe vocabulary terms (Term, Program, Evaluation Plan, Optimizer).

Discussed in: Evaluation Semantics

Event

A specific physical catastrophe in a model’s event catalog (e.g., a Cat 4 hurricane making landfall in Miami). Events have rates, metadata, and catalog IDs (event_id). In an ELT, each row is an event. In a SELT, the event_id column references the catalog. An event may produce losses across multiple LOBs and geographies.

See also: Occurrence, ELT

Discussed in: The Scenario Worldview

Exhaustion Probability

The probability that a loss reaches or exceeds the attachment point plus the limit of a contract layer — i.e., the layer is fully exhausted. Formally: $P_{\text{exhaust}} = \frac{1}{N} \sum_{s=1}^{N} \mathbf{1}[L_s \geq A + \ell]$ . The ratio of exhaustion probability to attachment probability reveals how “binary” a layer is.

See also: Attachment Probability, Limit

Discussed in: Metrics

Excess of Loss

A non-proportional reinsurance structure where the reinsurer pays losses above an attachment point up to a limit. The most common form is the CatXoL.

See also: Quota Share

Discussed in: Products and Contracts

F

Filter

A term operator that selects a subset of SELT rows matching specified predicates on categorical columns (peril, region, line of business). Pointwise — operates independently on each row. The first operator in most contract compositions, restricting the scope of downstream transformations.

Discussed in: Term Algebra

Facultative

A reinsurance contract that covers a single, individually underwritten risk, as opposed to a treaty which covers an entire book of business. Each facultative placement is negotiated separately. This site focuses primarily on treaty reinsurance.

See also: Treaty, Contract

Discussed in: Products and Contracts

Franchise Deductible

A deductible structure where, once the loss exceeds the threshold, the entire loss is covered — not just the excess. Contrasts with a standard deductible, which only pays the amount above the threshold. Modelled using the Trigger operator.

See also: Trigger

Discussed in: Term Algebra

Fronting

An arrangement where a licensed insurer issues policies on behalf of an unlicensed reinsurer or ILS fund, retaining little or no risk. The fronting company earns a fee for its regulatory license.

Discussed in: Market Participants

G

Gross Loss

From the reinsurer’s perspective: the loss the reinsurer assumes after applying contract terms to the subject loss. From the cedent’s perspective, this same amount is their recovery. All loss perspectives on this site default to the reinsurer’s point of view unless stated otherwise.

See also: Subject Loss, Recoveries, Net Loss

Discussed in: Products and Contracts

Grouping

The set of columns by which a term operator aggregates loss data before applying its transformation. Determines the operator’s resolution level: {scenario_id, timestamp, event_id} for occurrence-level operations, {scenario_id} for aggregate-level operations. The grouping parameter (sometimes called erode_by) unifies what legacy systems implement as separate occurrence and aggregate operator types.

Discussed in: Term Algebra, Evaluation Semantics

H

Hard Market

A phase of the underwriting cycle characterized by rising prices, restricted capacity, and stricter terms — typically following a major catastrophe that depletes industry capital.

See also: Soft Market, Underwriting Cycle

Discussed in: The Market

Hazard

The natural or man-made phenomenon that can cause loss — for example, a hurricane, earthquake, or flood. Used in catastrophe modelling to describe the physical event.

I

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, sidecars, and collateralized reinsurance.

Discussed in: Market Participants

Inuring

A dependency relationship between reinsurance contracts where one contract’s ceded loss is subtracted from the gross loss before another contract operates. The dependent contract sees a reduced (net-of-inuring) loss. The computation is: net_of_inuring = gross - ceded_by_inuring_contract. Inuring relationships create edges in the portfolio’s dependency graph.

See also: Sourcing, Dependency Graph

Discussed in: Expression Composition

L

Layer

A specific band of coverage within an excess-of-loss structure, defined by its attachment point and limit. A contract described as “$30M xs $20M” defines a layer from $20M to $50M. Multiple layers are typically stacked together within a program.

See also: Layer Function, Program

Discussed in: Products and Contracts (conceptual), Term Algebra (formal)

Layer Function

The most fundamental composition in reinsurance: $\text{Layer}(A, \ell) = \text{Cap}(\ell) \circ \text{Threshold}(A)$ , where $A$ is the attachment point and $\ell$ is the limit. Applies the threshold first (removing losses below $A$ ), then the cap (capping the excess at $\ell$ ). Every excess of loss contract uses this composition at its core.

See also: Layer, Threshold, Cap

Discussed in: Term Algebra

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

Discussed in: Products and Contracts

Loss Ratio

The ratio of expected loss to premium: $\text{LR} = \text{EL} / \text{Premium}$ . A loss ratio above 100% means the reinsurer expects to lose money on average. Used as a quick profitability indicator.

Discussed in: Capital and Pricing

M

Marginal Impact

The change in a portfolio-level metric (such as TVaR or capital requirement) caused by adding or removing a single contract.

See also: Marginal Pricing

Discussed in: Quantification (concept), Marginal Pricing (application)

Marginal Pricing

A pricing approach that computes the 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 Impact, Technical Premium

Discussed in: Marginal Pricing

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 scenarios — synthetic futures that form the basis for all downstream analytics. The output is a SELT.

See also: Scenario, SELT, Catastrophe Model

Discussed in: The Scenario Worldview

N

Net Loss

Gross loss minus recoveries — what actually stays on the reinsurer’s books after all outward protections. Also called retained loss.

See also: Gross Loss, Recoveries, Retained Loss

Discussed in: Products and Contracts

No Claims Bonus

A premium adjustment that returns a portion of premium to the cedent if losses remain below a defined threshold during the contract period. Implemented as a conditional Scale operator on the premium side.

Discussed in: Expression Composition

Non-Proportional Reinsurance

A reinsurance structure where the reinsurer pays only when losses exceed a threshold. Includes excess of loss, CatXoL, and aggregate stop loss contracts.

See also: Proportional Reinsurance

Discussed in: Products and Contracts

O

Occurrence

A discrete instance of loss within a simulated scenario — one catalog event appearing in one scenario. Identified by the composite key (scenario_id, timestamp, event_id) in the SELT. Each SELT row is an occurrence. OEP = Occurrence Exceedance Probability (largest single occurrence per scenario). Occurrence-level operators use grouping {s,t,e}.

See also: Event, Scenario, SELT, OEP

Discussed in: Quantification

OEP (Occurrence Exceedance Probability)

EP curve based on the largest single occurrence loss per scenario. Contrasts with AEP, which uses total aggregate loss.

Discussed in: Quantification

Optimizer

A system component that rewrites a program into a faster evaluation plan without changing the numerical result. Optimizations include fusing adjacent operators, pruning dead branches, and reordering independent computations. One of the four NDA-safe vocabulary terms (Term, Program, Evaluation Plan, Optimizer).

Discussed in: Evaluation Semantics

P

Participation

The percentage share of a layer or contract that a single reinsurer takes. A layer is typically placed with multiple reinsurers, each taking a participation (e.g. 50%, 30%, 20%). Each participant receives its share of the premium and pays its share of claims. The contract terms apply to the full loss first; the participation determines how the resulting ceded amount is divided.

See also: Layer, Program

Discussed in: Products and Contracts

PML (Probable Maximum Loss)

An estimate of the largest loss a portfolio or risk is expected to sustain from a single occurrence, typically at a specified return period (e.g., the 1-in-250 year PML). Used by reinsurers, rating agencies, and regulators to set risk limits and assess capital adequacy.

See also: OEP, VaR, Capital Requirement

Discussed in: Personas

Peril

A specific cause of loss such as wind, earthquake, flood, or wildfire. Catastrophe models are typically organized by peril.

Portfolio

A collection of reinsurance contracts held by a reinsurer. Portfolio-level analytics (diversification, marginal impact, capital allocation) are a core concern of this site.

Discussed in: Products and Contracts (conceptual), Quantification (formal)

Profit Commission

A commission paid by the reinsurer to the 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.

Discussed in: Expression Composition

Program

The entire structured set of reinsurance protections a cedent purchases for a given line of business. A program typically consists of multiple XoL layers stacked together, possibly combined with other sections such as a quota share, and represents the cedent’s overall reinsurance strategy for that risk category. A cedent may have several programs (e.g. a property catastrophe program, a casualty program). In engineering terms, a program is the ordered term operator sequence $C = T_k \circ \cdots \circ T_1$ that the engine compiles into an evaluation plan. One of the four NDA-safe vocabulary terms (Term Operator, Program, Evaluation Plan, Optimizer).

See also: Layer, Contract, Treaty

Discussed in: Products and Contracts (business), Engineering (formal)

Projection

A term operator that aggregates SELT rows by a subset of columns, summing the loss values. Reduces dimensionality — for example, collapsing occurrence-level rows to scenario-level totals. Scenario-aggregating by nature.

Discussed in: Term Algebra

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 and surplus share treaties.

See also: Non-Proportional Reinsurance

Discussed in: Products and Contracts

Q

A 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, Excess of Loss

Discussed in: Products and Contracts

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.

Discussed in: Capital and Pricing

Rate on Line (ROL)

The ratio of premium to 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.

Discussed in: Capital and Pricing

Reinstatement

The restoration of coverage after a loss has eroded the limit, typically requiring an additional premium. Introduces intra-scenario statefulness into contract evaluation — the response to a subsequent occurrence depends on what prior occurrences consumed. With $n$ reinstatements, the aggregate limit becomes $\text{limit} \times (1 + n)$ .

Discussed in: Products and Contracts (conceptual), Expression Composition (implementation)

Reinsurance

A risk transfer mechanism where an insurance company (the cedent) purchases coverage from a reinsurer, transferring a portion of its exposure to catastrophic or accumulated losses. Enables insurers to write more business, stabilize earnings, and meet regulatory capital requirements.

Discussed in: The Market

Reinsurer

A company that provides insurance to insurance companies, absorbing a portion of their risk in exchange for premium.

See also: Cedent, Retrocession

Discussed in: Market Participants

Recoveries

What the reinsurer gets back from its own outward protections. Includes traditional retrocession (ceded loss) as well as parametric instruments such as ILWs and cat bonds. Gross loss minus recoveries equals net loss. Note: from the cedent’s perspective, “recoveries” refers to what they receive from the reinsurer — which is the reinsurer’s gross loss.

See also: Gross Loss, Net Loss, Ceded Loss

Discussed in: Products and Contracts

Retained Loss

Synonym for net loss — what stays on the reinsurer’s books after recoveries.

See also: Net Loss, Gross Loss

Discussed in: Products and Contracts

Retention

The amount of risk or loss that the cedent keeps rather than transferring to the reinsurer. In an excess of loss contract, typically the attachment point.

Discussed in: Products and Contracts

Retrocession

Reinsurance purchased by a reinsurer — “reinsurance of reinsurance.” The seller of retrocession is called a retrocessionaire.

Discussed in: The Market, Market Participants

Risk

The potential for financial loss arising from an uncertain event. In reinsurance, usually refers to the quantified probability and severity of catastrophe losses.

S

Scale

A term operator that multiplies every loss value in a SELT by a constant factor. Pointwise — operates independently on each row. Used to model quota share cession percentages: Scale(0.25) transfers 25% of every loss.

Discussed in: Term Algebra

Scenario

A single simulated year of catastrophe activity drawn from a probabilistic model. Each scenario contains one or more occurrences (each identified by the composite key (scenario_id, timestamp, event_id)). Identified by scenario_id in the SELT. All scenarios are typically equiprobable.

Discussed in: Quantification

Scenario Isolation

The evaluation principle that each scenario is processed independently — no information crosses scenario boundaries. This guarantees embarrassingly parallel evaluation and ensures that the response to one simulated year never influences another.

Discussed in: Evaluation Semantics

SELT (Scenario Event Loss Table)

The fundamental data structure for catastrophe risk analytics — a table with columns (scenario_id, timestamp, event_id, peril, geography_id, lob_id, loss). Each row represents an occurrence — a discrete loss instance within a simulated scenario, referencing a catalog event at a given LOB and geographic resolution. Losses are organized by scenario, occurrence, and sub-dimensions.

See also: ELT

Discussed in: Quantification (formal), foreshadowed in Personas

Sidecar

A special-purpose vehicle that allows third-party investors to participate in a reinsurer’s underwriting results, sharing both premium and losses.

Discussed in: Market Participants

Sliding Scale Commission

A 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. Aligns incentives between cedent and reinsurer.

See also: Ceding Commission, Profit Commission

Discussed in: Expression Composition

Soft Market

A phase of the underwriting cycle characterized 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, Underwriting Cycle

Discussed in: The Market

Sourcing

A dependency relationship between reinsurance contracts where one contract operates on another contract’s ceded output. Contrasts with inuring, where the dependent contract sees reduced gross loss. In sourcing, the retro contract transforms the source contract’s ceded losses. Sourcing relationships create edges in the portfolio’s dependency graph.

See also: Inuring, Dependency Graph, Retrocession

Discussed in: Expression Composition

Standard Deviation

A measure of the dispersion of scenario losses around the expected loss. Formally: $\sigma = \sqrt{\frac{1}{N} \sum_{s=1}^{N} (L_s - \text{EL})^2}$ , using the population formula ( $1/N$ ) because the scenarios represent the entire simulated probability space. Appears in simpler pricing models (e.g., the standard deviation loading principle).

See also: EL, VaR, TVaR

Discussed in: Metrics

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. Sub-additivity is a defining property of coherent risk measures. TVaR always satisfies sub-additivity; VaR does not.

See also: TVaR, VaR

Discussed in: Metrics

Subject Loss

The loss entering a contract from the cedent’s book — the input that contract terms (attachment, limit, cession rate) operate on. From the reinsurer’s perspective, the subject loss is what the cedent presents; the contract terms transform it into the reinsurer’s gross loss.

See also: Gross Loss, Net Loss

Discussed in: Products and Contracts

A 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 a per-policy variable Scale operator.

See also: Quota Share, Proportional Reinsurance

Discussed in: Expression Composition

T

Technical Premium

The minimum premium that covers expected loss, operating expenses, and the 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).

Discussed in: Capital and Pricing

Term Operator

A pure function that transforms loss data — the atomic building block of contract definitions. Takes a SELT as input and produces a SELT as output. Classified by state scope: pointwise (row-independent), occurrence-aggregating (groups by {scenario_id, timestamp, event_id}), scenario-aggregating (groups by {scenario_id}), or portfolio (crosses scenario boundaries). Operators compose into programs.

See also: Program, Layer Function

Discussed in: Term Algebra (definitions), Expression Composition (composition)

Threshold

A term operator that removes losses below a specified level. Formally: computes the grouped total, subtracts the threshold, takes the positive part, and distributes the result back to individual rows proportionally. Parameterized by a level and a grouping that determines whether the threshold applies per occurrence or per scenario (aggregate).

See also: Cap, Layer Function

Discussed in: Term Algebra

Trigger

A term operator that passes the full loss through when a condition is met and returns zero otherwise. Unlike Threshold, which removes the portion below the level, Trigger is binary: all or nothing. Used for franchise deductibles, parametric structures, and conditional activations.

See also: Franchise Deductible

Discussed in: Term Algebra

Treaty

A contract that covers a defined book of business over a set period (usually 12 months, renewing annually), as opposed to 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, Layer, Program

Discussed in: Products and Contracts

TVaR (Tail Value at Risk)

The average loss in the worst scenarios beyond the VaR threshold — a measure of tail severity, not just tail probability. Preferred over VaR for capital thinking because it captures the magnitude of extreme losses. Formally: $\text{TVaR}_\alpha = \frac{1}{k}\sum_{r=1}^{k} L_{(r)}$ where $L_{(r)}$ is the $r$ -th largest loss and $k = \lfloor N(1-\alpha) \rfloor$ .

Discussed in: Quantification

U

Underwriting Cycle

The cyclical pattern of the reinsurance market alternating between hard and soft phases, driven by the interaction of catastrophe losses, capital flows, and competitive dynamics. Typically spans 5-10 years.

Discussed in: The Market

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 loss (EP curve convention). At the 99% confidence level, VaR is the loss exceeded in 1 out of 100 scenarios.

See also: TVaR, EP Curve

Discussed in: Quantification

Vendor Model

A catastrophe model developed by a specialist vendor (such as Moody’s RMS, Verisk AIR, or CoreLogic) and offered as a commercial product.

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. 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 pricing layers that sit in a specific band of the return period spectrum, differentiating frequency-driven from severity-driven risk, and allocating capital to specific portions of the loss distribution.

See also: TVaR, VaR, EP Curve

Discussed in: Metrics