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.

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A

AEP (Aggregate Exceedance Probability)

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

Discussed in: Analytics Toolkit

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 — it is the attachment $A$ of an aggregate excess term.

Discussed in: Products and Contracts (conceptual), Analytics Toolkit (formal)

Aggregate Stop Loss

A reinsurance contract that caps the cedent’s total annual losses above an aggregate deductible. Applies at the trial (annual) level rather than per occurrence. In term notation: $\text{agg}_{\text{excess}}(A, \ell)$ applied to the trial total.

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 term notation: $\text{agg}_{\text{excess}}(A, \ell)$ applied to the trial total.

See also: CatXoL, Aggregate Stop Loss

Discussed in: Products and Contracts, AggXoL

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: $P_{\text{attach}} = \frac{1}{N} \sum_{j=1}^{N} \mathbf{1}[L_j > A]$. A layer with 30% attachment probability means the reinsurer expects to pay a claim roughly 3 years out of 10.

See also: Exhaustion Probability, Attachment Point

Discussed in: Metrics

B

Back-Allocation

Distributing losses computed at a grouped (aggregate) level back to the original higher-resolution records — also called disaggregation. 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: Aggregate and disaggregate

Book (of Business)

The set of risks a cedent has underwritten — the policies whose losses are the 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, which is the reinsurer’s collection of contracts: a reinsurer’s portfolio is assembled from pieces of many cedents’ books.

See also: Subject Loss, Cedent, Portfolio

Discussed in: Risk profiling

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 a small share of premium.

Discussed in: Market Participants

Burning Cost

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

Discussed in: Metrics

C

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

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 TELT 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 term notation: $\text{occ}_{\text{excess}}(A, \ell)$ applied to each occurrence independently.

See also: Excess of Loss, AggXoL

Discussed in: Products and Contracts, CatXoL

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.

See also: Profit Commission, Sliding Scale Commission

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: Analytics Toolkit

Composition

A contract’s definition as financial terms combined into a single transformation — both the act of combining the terms and the result. Written $C = T_k \circ \cdots \circ T_1$: the formula reads right to left ($T_1$ applies first), while data flows left to right through the composition. When a contract feature’s dataflow branches (for example, reinstatement premiums consume the occurrence-layer output alongside the loss path), the shared intermediate is named and the composition is written as several equations. Compositions connected by inuring or sourcing relationships form a dependency graph — the graph is a property the engine discovers, not the way contracts are written down.

See also: Contract, Program

Discussed in: Contracts as compositions

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 Financial Modelling chapter, a contract is formally modelled as an ordered composition of financial terms applied to input loss data.

See also: Treaty, Layer, Composition, Program

Discussed in: Products and Contracts (conceptual), Contracts as compositions (formal)

CTE (Conditional Tail Expectation)

Synonym for TVaR. The expected loss conditional on being in the worst $(1-\alpha)$ of trials. 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

Damage Ratio

Modelled loss expressed as a fraction of the 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 TELT 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.

See also: TIV, TELT

Discussed in: The Trial Worldview, Risk profiling

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 graph is discovered by tracing dependencies, not authored: contracts are written as compositions, and the graph is a property of how they connect.

Discussed in: Programs

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: Analytics Toolkit

E

EL (Expected Loss)

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

Discussed in: Metrics

ELT (Event Loss Table)

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

Discussed in: Analytics Toolkit

ES (Expected Shortfall)

Synonym for TVaR. The expected loss conditional on being in the worst $(1-\alpha)$ of trials. 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: Analytics Toolkit

Expiry

The date on which a reinsurance contract’s coverage period ends. Losses from events after the expiry are not covered by the contract. The coverage period runs from inception to expiry.

See also: Inception, In-force

Discussed in: Contract period

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

Event

A prototypical physical catastrophe in a model’s event catalog, with fixed physical characteristics — for example, a Cat 4 hurricane on a defined track making landfall in Miami. Events carry rates, metadata, and catalog IDs (event_id). The catalog is shared across all trials: different trials draw different mixtures of catalog events as their occurrences, so the same event can recur in many trials at different dates and loss scales. In an ELT, each row is an event; in a TELT, the event_id column references the catalog. One event may produce losses across multiple LOBs and geographies.

See also: Occurrence, ELT

Discussed in: The Trial 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: $P_{\text{exhaust}} = \frac{1}{N} \sum_{j=1}^{N} \mathbf{1}[L_j \geq A + \ell]$. 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 financial term that selects the subset of TELT rows matching specified predicates on categorical columns (peril, geography, line of business). Operates independently on each row. The first term in most contract compositions, restricting the scope of downstream transformations.

Discussed in: Loss filter

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

Financial Modelling

The process of applying contract terms to subject losses to produce the reinsurer’s 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, CatXoL, AggXoL — defines a different transformation.

Discussed in: Financial Modelling

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 term.

See also: Trigger

Discussed in: Products and Contracts, Trigger

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

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

In-force

A contract that is currently within its coverage 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 date but still in-force from the reinsurer’s perspective if it has outstanding claims on long-tail business.

See also: Inception, Expiry

Discussed in: Contract period

Inception

The date on which a reinsurance contract’s coverage period begins. Losses from events before inception are not covered. The coverage period runs from inception to expiry.

See also: Expiry, In-force

Discussed in: Contract period

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: Programs

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. The layer payout function $\min(\max(L - A, 0), \ell)$ is the core of the occurrence excess and aggregate excess terms.

See also: Program, Attachment Point, Limit

Discussed in: Products and Contracts (conceptual), 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

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

Loss Set

One catastrophe model run’s loss output, delivered and validated as a unit — a TELT covering one peril or model view for a submission. 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.

See also: TELT, Submission, Catastrophe Model

Discussed in: Risk profiling

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: Analytics Toolkit (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 trials — synthetic futures that form the basis for all downstream analytics. The output is a TELT.

See also: Trial, TELT, Catastrophe Model

Discussed in: The Trial 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.

Discussed in: Products and Contracts

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 dated instance of a catalog event within a trial — the realized appearance of an event at a specific time in one simulated future. Identified by the composite key (trial_id, timestamp, event_id) in the TELT. Each TELT row is an occurrence. The event is the reusable prototype; the occurrence is its dated, trial-specific realization. OEP = Occurrence Exceedance Probability (largest single occurrence per trial).

See also: Event, Trial, TELT, OEP

Discussed in: Analytics Toolkit

OEP (Occurrence Exceedance Probability)

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

Discussed in: Analytics Toolkit

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), Analytics Toolkit (formal)

Post-Model Report

The write-up of catastrophe model output that a cat modeller prepares for an underwriter: a characterization of a cedent’s exposure and subject loss — loss-set reconciliation, exposure summary, and risk metrics — before any contract is applied. The name varies by organization (modelling summary, account analytics report); the artifact is universal.

See also: Submission, Loss Set, Subject Loss

Discussed in: Risk profiling

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.

See also: Ceding Commission, Sliding Scale Commission

Discussed in: Products and Contracts

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). The contracts within a program are each a composition of financial terms, and may be related to one another through inuring or sourcing. “Program” is used in this business sense only — the assembled term structure of a single contract is a composition, not a program.

See also: Layer, Contract, Treaty, Composition

Discussed in: Products and Contracts

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

Quota Share

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-trial statefulness into contract evaluation — the response to a subsequent occurrence depends on what prior occurrences consumed. With $n$ reinstatements, the aggregate limit becomes $\text{limit} \times (1 + n)$.

Discussed in: Products and Contracts (conceptual), CatXoL (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

Scaling

A financial term that multiplies every loss value in a TELT by a constant factor. Operates independently on each row. Used to model quota share cession percentages and participation: $\text{scale}(0.25)$ transfers 25% of every loss.

Discussed in: Scaling

Scenario (stress test)

A deliberately chosen set of assumptions or parameters used for what-if and stress analysis — for example, “a Cat 5 hits Miami and capital markets fall 30% in the same year.” Distinct from a trial: a trial is a random draw from the loss model, whereas a scenario is a hand-specified state of the world. This site reserves the word “scenario” for stress testing and what-if analysis; the unit of simulated loss data is a trial, not a scenario.

See also: Trial

Discussed 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

Sign Convention

The choice of whether monetary losses are represented as positive or negative values in loss data. This site is loss-positive: loss and tiv are strictly positive in a base TELT (model output), non-negative in transformed TELTs (operator outputs may contain legitimate zeros), and a negative loss anywhere is a validation error — other financial record types are a schema extension, never a sign flip. The convention determines the sort order of the loss distribution, which end is the tail, how ranks map to return periods, and whether losses and premiums net by addition or by explicit subtraction. Mixing conventions when integrating data from multiple sources is a frequent cause of silent numerical errors.

See also: TELT, EP Curve, VaR

Discussed in: The Trial Worldview, Metrics

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: Products and Contracts

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: Programs

Standard Deviation

A measure of the dispersion of trial losses around the expected loss. Formally: $\sigma = \sqrt{\frac{1}{N} \sum_{j=1}^{N} (L_j - \text{EL})^2}$, using the population formula ($1/N$) because the trials 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

Submission

The package a cedent — usually via its 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 that analytics operates on.

See also: Cedent, Broker, Loss Set, Post-Model Report

Discussed in: Risk profiling

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

Surplus Share

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 per-policy variable scaling.

See also: Quota Share, Proportional Reinsurance

Discussed in: Quota share

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

TELT (Trial Event Loss Table)

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

See also: ELT, Trial

Discussed in: Analytics Toolkit (formal), foreshadowed in Personas

Term (Financial Term)

A self-contained transformation of loss data — the atomic building block of contract definitions. Takes a TELT as input and produces a TELT as output, with no side effects or hidden state. The site’s term catalog includes the loss filter, contract period, scaling, occurrence excess, and aggregate excess. Terms combine into compositions — a contract is a composition of terms.

See also: Composition, Contract

Discussed in: Contracts as compositions

TIV (Total Insured Value)

The sum of insured values of the exposure a TELT row touched, at that row’s geography and LOB resolution — the tiv column. TIV is the denominator of the damage ratio. The TELT 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, TELT

Discussed in: The Trial Worldview, Risk profiling

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) or an external index (industry loss warranty, parametric structures).

See also: Franchise Deductible

Discussed in: Trigger

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

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 TELT. Trials are typically equiprobable, each representing $1/N$ of the simulated probability space. The word “trial” is reserved for this random-draw unit; a deliberately chosen what-if state is a scenario.

See also: TELT, Event, Occurrence

Discussed in: Analytics Toolkit

TVaR (Tail Value at Risk)

The average loss in the worst trials 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: Analytics Toolkit

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 trials.

See also: TVaR, EP Curve

Discussed in: Analytics Toolkit

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