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.

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. 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).

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: Exceedance probability curves

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), Aggregate excess (formal)

Aggregate Excess

A financial term that applies an attachment $A$ and a limit $\ell$ to a trial’s 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 because each occurrence row carries its erosion of the layer, in claims order. The occurrence excess applies the same layer to each occurrence independently.

Discussed in: Aggregate excess, AggXoL

Aggregate Limit

The cap on what a contract pays across a whole trial: the $\ell$ of an aggregate excess. A CatXoL always carries one, because $n$ reinstatements cap the period’s recoveries at $(1 + n) \cdot \ell$ . Contrast the 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, Event Limit, Aggregate Deductible

Discussed in: Dissecting a contract, AggXoL, Quota share

Aggregate Stop Loss

A reinsurance contract that caps the cedent’s total annual losses above an aggregate deductible: the same structure this site models as an AggXoL, whose entry states what separates the two names.

See also: AggXoL

Discussed in: Products and contracts (conceptual), AggXoL (formal)

AggXoL (Aggregate Excess of Loss)

A contract with attachment and limit applied to the total annual (aggregate) loss rather than per occurrence. The same operation as an 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.¹ In term notation: $\text{agg}_{\text{excess}}(A, \ell)$ applied to the trial total.

See also: Aggregate Excess, CatXoL, Aggregate Stop Loss

Discussed in: Products and contracts (conceptual), AggXoL (formal)

Alternative Capital

Non-traditional reinsurance capital sourced from capital markets via ILS structures, sidecars, or collateralised reinsurance. About 17% of global reinsurer capital at the end of 2025 ($136 billion of $785 billion), sourced on Market participants.

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 layer pays: the share of trials in which the loss exceeds the 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 read at $A$ counts with $\geq$ and gives the share of trials that reached the attachment, which differs wherever trials tie at $A$ .

Discussed in: Attachment and exhaustion 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: 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, Occurrence Excess, Aggregate Excess

Discussed in: 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 or a parametric cat bond.

See also: ILW, Trigger

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 Re (formerly Guy Carpenter), Gallagher Re, and Howden Re.

See also: Brokerage, Placement Slip, Submission

Discussed in: Market participants

Broker Market

The reinsurers that write through intermediaries, as against the direct market, which deals with cedents itself. A cedent reaches the broker market through a broker, who carries the submission, collects the quotes, and settles the firm order terms. This site’s convention: broker market, where IRMI and much of the market say brokerage market, because on this site brokerage is the fee.

Also known as: brokerage market

See also: Broker, Direct Market, Underwriting Workflow

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

Brokerage Market

See 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). 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

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: 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.

Discussed in: Portfolio analytics

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 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.

Also known as: unexpected loss

Discussed in: Standalone program pricing

Cat Bond

An insurance-linked security 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.²

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 YELT 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: $\text{CatXoL}(A, \ell, n) = \text{agg}_{\text{excess}}(0,\, (1{+}n) \cdot \ell) \circ \text{occ}_{\text{excess}}(A, \ell)$ , the occurrence layer applied to each occurrence independently, capped for the period by an aggregate limit that encodes $n$ reinstatements (the scoping loss filter and contract period elided).

Discussed in: Products and contracts (conceptual), 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 (the same dollars, seen from opposite sides). In the site’s dominant usage the cedent cedes to the reinsurer. When a reinsurer cedes outward in turn, the same word names what it transfers through retrocession, a specific type of recovery.

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), 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 that varies with the ceded book’s loss ratio between a stated minimum and maximum.³

Cession Percentage

The proportion of risk (and premium) transferred from cedent to reinsurer in a proportional contract such as a 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, which records the reinsurer’s share of the placement and is applied at roll-up.

See also: Quota Share, Participation, Scaling

Discussed in: Quota share, 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. 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 is the risk delta, the change in the tail from adding the contract.

See also: TVaR, Marginal TVaR, Euler Allocation

Discussed in: Financial perspectives, Portfolio analytics

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 ( $\rho(X + Y) \leq \rho(X) + \rho(Y)$ ), 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 is coherent; VaR satisfies three of the four and fails sub-additivity.

See also: Sub-additivity, TVaR, VaR

Discussed in: VaR vs. TVaR

Collateralised Reinsurance

A reinsurance 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, rather than by a rated reinsurer’s balance sheet. The loss-side analytics are those of the equivalent traditional contract; only the capital behind it differs.

See also: Alternative Capital, Fronting

Discussed in: Market participants

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 or forwarding form a dependency graph, which this site derives from the clauses rather than storing separately. Distinct from a program, which is the business grouping of contracts.

See also: Term, Contract, Program

Discussed in: Contracts as compositions

Contract

The generic term for any reinsurance agreement, the legal document formalising 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)

Contract Lifecycle

The states of one contract over time: quoted, bound, in-force from inception to expiry, expired, and in runoff while claims remain open. It covers the same ground as the later steps of the underwriting workflow, seen from the contract instead of from the people working on it.

Contract Period

The window from a contract’s inception to its expiry, and the financial term that enforces it: a date-range check that keeps only the occurrences whose timestamp falls inside the window, on a 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, Expiry, Losses Occurring, Term

Discussed in: 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). Used to compute the capital charge component of the technical premium: Capital Cost = Capital Requirement × Cost of Capital Rate.

See also: Capital Requirement, Technical Premium, RAROC

Discussed in: Standalone program pricing

Covered Loss

The covered, in-period slice of the subject loss: what remains after a contract’s filter and 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, Gross Loss, Filter

Discussed in: Financial perspectives

CTE (Conditional Tail Expectation)

The expected loss conditional on the loss being at or above the VaR threshold. Coincides with TVaR and Expected Shortfall (ES) 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. Where this site uses the name, it computes the rank-based TVaR; Metrics compares this divergence with ES’s.

Discussed in: Tail Value at Risk

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 YELT 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, YELT

Discussed in: The trial worldview, Risk profiling

Demo Tier

This site’s 20-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, loss ratio, RAROC) demonstrates method rather than a market benchmark.

See also: Trial, YELT

Discussed in: The trial worldview

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 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

Direct Market

The reinsurers that deal with cedents themselves rather than through an intermediary, as against the broker market, where a broker carries the submission, collects the quotes, and settles the firm order terms.

See also: Broker, Brokerage, Underwriting Workflow

Discussed in: Market participants

Disaggregation

Another name for 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 measured standalone. A well-diversified portfolio requires less capital than the sum of its parts, sourced on Personas.

Discussed in: Portfolios, Portfolio analytics

Double Recovery

The same dollar of loss recovered under two contracts. Within a program it is prevented by 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, Program

Discussed in: Programs

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, 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, Technical Premium, Loss Ratio

Discussed in: 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, exposure values) and naming varies. Unlike a YELT, 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, Event

Discussed in: The trial worldview

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 and AEP.

Discussed in: Exceedance probability curves

Erosion

The progressive consumption of an aggregate layer as a trial’s occurrences accumulate against its attachment and 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’s gross loss by erosion keeps its output a YELT. Erosion is 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.

Discussed in: Aggregate excess

ES (Expected Shortfall)

The average loss in the worst $(1-\alpha)$ of the distribution. The name used for TVaR in banking regulation and the risk-measure literature. Coincides with TVaR and Conditional Tail Expectation (CTE) 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

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.

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. Each dated appearance of an event inside a trial is an occurrence, so one event recurs in many trials at different dates. In an ELT each row is an event; in a YELT the event_id column references the catalog.

See also: Occurrence, ELT

Discussed in: The trial worldview

Event Limit

A cap applied to each occurrence before any later term acts on it: an occurrence excess with zero attachment. Used on quota share contracts, where it caps each occurrence before the 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, which caps the period total.

See also: Aggregate Limit, Limit, Quota Share

Discussed in: Quota share

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

Exhaustion Point

The top of a layer, $A + \ell$ : the loss level at which the limit is fully consumed and the contract pays no more. Losses above it fall back to the cedent, which is why an excess-of-loss retention has two parts: everything below the attachment point and everything above the exhaustion point.

Discussed in: Products and contracts

Exhaustion Probability

The probability that a layer is fully consumed: the share of trials in which the loss reaches or exceeds the attachment point plus the 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. The inequality is $\geq$ where attachment’s is strict: a loss exactly at $A + \ell$ pays the full limit.

Discussed in: Attachment and exhaustion probability

Expiry

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

See also: Inception, In-force

Discussed in: Contract period

Exposure Management

The control of catastrophe risk at the level of a whole 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 performs, whatever title an organisation gives the role.

See also: Portfolio Manager, Portfolio, Roll-up

Discussed in: Portfolio analytics

F

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: Dissecting a contract

Forwarding

A dependency between reinsurance contracts in which one contract forwards its ceded output to another as that contract’s subject loss, as an inward contract does to the retrocession that protects it. Contrast 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.

See also: Inuring, Dependency Graph, Retrocession

Discussed in: Programs

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, a term the contract catalog does not have yet.

See also: Trigger

Discussed in: Products and contracts

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 licence.

See also: Collateralised Reinsurance

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 ceded loss. 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 market cycle characterised by rising prices, restricted capacity, and stricter terms, typically following a major catastrophe that depletes industry capital.

See also: Soft Market, Market Cycle

Discussed in: Market participants

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.

Hours Clause

A treaty clause that defines one loss 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, 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, Occurrence, Event

Discussed in: 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

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 collateralised reinsurance.

See also: ILS Fund, Alternative Capital

Discussed in: 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, sidecars, and collateralised reinsurance. It supplies reinsurance capacity without a rated balance sheet, which is why the limit it sells is collateralised.

See also: ILS, Alternative Capital, Fronting

Discussed in: Market participants

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. Reinsurers use ILWs as outward protection alongside retrocession and cat bonds. Its condition is a trigger evaluated against an external index instead of the contract’s own subject loss.

See also: Basis Risk, Trigger, Recoveries, Cat Bond

Discussed in: Financial perspectives

In-force

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

See also: Inception, Expiry, Runoff, Contract Lifecycle

Discussed in: Contract period

Inception

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

See also: Expiry, In-force

Discussed in: Contract period

Inuring

A dependency between reinsurance contracts in which one contract’s gross loss is subtracted from another contract’s 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, where the dependent contract takes the other’s ceded output as its input. Both relationships are edges of the dependency graph.

See also: Forwarding, Double Recovery, 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

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 schema it is a column, and one of the dimensions a filter can scope a contract to. A single occurrence commonly spans several lines of business, which is why occurrence-level terms group their rows before they act.

See also: YELT, Filter, Book (of Business)

Discussed in: The trial worldview

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 from the reinsurer’s perspective long after expiry. Out of scope for this site, which treats short-tail property catastrophe business.

See also: Short-Tail, Runoff, IBNR

Discussed in: Contract period

Loss Corridor

A loss-sensitive feature of a proportional contract: a band (customarily of loss ratio, sometimes of currency) within which the 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 is).

See also: Quota Share, Loss Ratio, Aggregate Deductible

Discussed in: 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 compositions, restricting the scope of downstream transformations.

See also: Contract Period, Term

Discussed in: Loss filter

Loss Ratio

This site’s convention: the ratio of modelled 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. The industry’s accounting definition is the realised ratio of incurred loss to earned premium;⁴ 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, Rate on Line, Technical Premium

Discussed in: Standalone program pricing

Loss Set

One catastrophe model run’s loss output, delivered and validated as a unit: a YELT covering one peril or model view for a 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 and TVaR in general do not.

See also: YELT, Submission, Catastrophe Model

Discussed in: Risk profiling

Losses Occurring

The coverage basis on which a contract responds to losses by the date of the event: an occurrence is covered when it falls between inception and expiry, whichever policy it arose under. The basis this site assumes throughout and the one its contract period term implements: the only one a YELT can express, since it needs no more than the occurrence timestamp. The contrasting bases are risks attaching and underwriting year; both need each loss’s original policy inception date, which a YELT row does not carry.

Discussed in: Contract period

M

Marginal Impact

The change in a portfolio-level metric caused by adding or removing one contract. Measured on TVaR it is the Marginal TVaR; measured on the capital requirement it is the $\Delta K$ of 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, Marginal Pricing

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.

Marginal TVaR

The change in a portfolio’s TVaR 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 measured on TVaR, and the decision to add the contract depends on it.⁵ Co-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, Marginal Impact, Marginal Pricing

Discussed in: Additional metrics

Market Cycle

The alternation of the reinsurance market between hard and soft phases, driven by catastrophe losses, capital flows, and competition. Its period is irregular. Not the 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, Soft Market, Renewal Cycle

Discussed in: Market participants

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 YELT.

See also: Trial, YELT, 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. Market usage sometimes calls this the reinsurer’s “retained loss”; this site reserves retained for the cedent’s side (see 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

Nth-Event Cover

A catastrophe excess-of-loss contract meant to respond only from the second (or a later) occurrence of the 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 and 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 and contract period elided).⁶ 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: 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.

Discussed in: Contract catalog

O

Occurrence

A dated instance of a catalog event within a 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. 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, Trial, YELT, OEP

Discussed in: The trial worldview

Occurrence Definition

The treaty wording that says what counts as one loss occurrence for per-occurrence terms: for property catastrophe, usually an hours clause per peril, sometimes restricted to a single named event. The per-occurrence formulas on this site take the YELT’s 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, Occurrence, Event

Discussed in: Occurrence excess

Occurrence Excess

A financial term that applies an attachment point $A$ and a limit $\ell$ to each 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 to the occurrence’s rows in proportion to their losses. It is the layer of a CatXoL and, with zero attachment, a quota share’s event limit. The aggregate excess applies the same shape to the trial total instead.

Discussed in: Occurrence excess, CatXoL

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: Exceedance probability curves

P

Participation

The percentage share of a layer or contract that one 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% and applies the share at roll-up. Distinct from the cession percentage, which is a term of a proportional contract.

See also: Roll-up, Cession Percentage, Layer, Program

Discussed in: Products and contracts (conceptual), Portfolios (formal)

Per-Risk Excess of Loss

An excess-of-loss contract whose attachment point and 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.

See also: Excess of Loss, CatXoL

Discussed in: Products and contracts

Peril

A specific cause of loss such as wind, earthquake, flood, or wildfire. Catastrophe models are typically organised by peril, and this site’s YELT 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) and that the participating reinsurers sign. It is written in business language, so encoding it as a composition of terms is an act of interpretation.

Also known as: slip (trade jargon)

See also: Broker, Underwriting Workflow

Discussed in: Market participants

PLT (Period Loss Table)

Moody’s RMS’s name for the YELT.

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

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), Portfolios (formal)

Portfolio Manager

The role responsible for the reinsurer’s 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, Roll-up

Discussed in: Portfolio analytics

Post-Model Report

The write-up of catastrophe model output that a cat modeller prepares for an underwriter: a characterisation 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 organisation (modelling summary, account analytics report); the artifact is universal.

See also: Submission, Loss Set, Subject Loss

Discussed in: Risk profiling

Primary Uncertainty

Whether and how often a catalog event occurs; defined with its counterpart under secondary uncertainty.

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: Products and contracts

Program

The structured set of reinsurance protections bought to cover a defined exposure: most often a cedent’s property-catastrophe book, equally a reinsurer’s own retrocession or a single large risk. It typically stacks several excess-of-loss layers into a tower, sometimes beside a quota share. The contracts in a program are each a composition, independent of one another in a plain tower and related through inuring or 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, Layer, Contract, Composition, Retrocession

Discussed in: Products and contracts (conceptual), 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 and surplus share contracts.

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 (conceptual), 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 and $K$ is measured on the outcome net of it.

Discussed in: Standalone program 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.

See also: Limit, Technical Premium, Loss Ratio

Discussed in: Standalone program pricing

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

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 $\text{limit} \times (1 + n)$ , a claims-side encoding 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.

Discussed in: Products and contracts (conceptual), CatXoL (formal)

Reinstatement Premium

The premium the cedent pays for a limit restored by a paid 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, Technical Premium

Discussed in: Reinstatement premium (formal), Standalone program pricing

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, stabilise 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

Renewal Cycle

The annual repetition of the 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, which has no fixed period.

Discussed in: Market participants

Renewal Period

The weeks before a common 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.

Also known as: renewal season

See also: Renewal Cycle, Inception

Discussed in: Market participants

Retained Loss

The cedent-side complement of the ceded loss on a contract: the part of the 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. The market also calls that position “retained loss”.

See also: Retention, Subject Loss, Net Loss

Discussed in: Products and contracts (conceptual), Financial perspectives (formal)

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. Like retained loss, retention always refers to the cedent’s side on this site.

See also: Retained Loss, Attachment Point

Discussed in: Products and contracts

Retrocession

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

Discussed in: The market, Market participants

Retrocessionaire

The seller of 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, not a schedule: a 1-in-200 loss can occur in two consecutive trials.

See also: EP Curve, VaR, TVaR

Discussed in: Metrics

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, which covers by event date. It needs each loss’s original policy inception date, which a YELT row does not carry, so this site’s contract period term cannot express it.

See also: Losses Occurring, Underwriting Year

Discussed in: Contract period

Roll-up

The operation that combines a portfolio’s contracts into one loss table: scale each contract’s gross loss to the reinsurer’s participation, then sum across contracts, $L_j^{\text{portfolio}} = \sum_i p_i\,C_i(L_j)$ . Summing per trial produces a YLT, enough for AEP metrics; summing per occurrence produces the portfolio YELT, needed for OEP metrics and for occurrence-term 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. 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, while VaR carries no such guarantee.

Discussed in: Portfolios, 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 while claims are still being settled, short for short-tail property catastrophe business and years long for long-tail lines. For a portfolio, a runoff view evaluates each contract over the part of its contract period that remains at the analysis date, with no renewals assumed, so the exposure declines as contracts expire.

See also: In-force, Expiry, Contract Lifecycle

Discussed in: Contract period

S

Scaling

A financial term that multiplies every loss value in a YELT by a constant factor. Operates independently on each row. The same operation carries two business meanings in two places: a quota share cession percentage inside a contract’s composition, and the participation share applied at roll-up. $\text{scale}(0.25)$ transfers 25% of every loss.

See also: Cession Percentage, Participation, Term

Discussed in: 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: 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, not scenarios.

See also: Trial

Discussed in: Personas

Secondary Uncertainty

The spread of loss given that a catalog event occurs: the distribution around the event’s mean loss, which a vendor ELT carries as standard-deviation columns beside the mean. Primary uncertainty is whether and how often the event occurs (the rate). A production YELT 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, YELT, Event

Discussed in: The trial worldview

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 alone, with no claims-development pattern. Contrast long-tail.

See also: Long-Tail, Runoff

Discussed in: Contract period

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 losses are stored as positive or negative values. This site’s convention: loss-positive. loss and tiv are strictly positive in a base YELT, 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, EP Curve, VaR

Discussed in: The trial worldview, If your losses are negative

Signing Down

The reduction of every reinsurer’s written line so that the participations 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, Broker, Underwriting Workflow

Discussed in: Products and contracts

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, between a stated minimum and maximum. Aligns incentives between cedent and reinsurer.

See also: Ceding Commission, Profit Commission

Discussed in: Products and contracts

Slip

Trade jargon for the placement slip.

Soft Market

A phase of the 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, Market Cycle

Discussed in: Market participants

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 ( $1/N$ ): 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, VaR, TVaR

Discussed in: Additional 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. It is one of the four axioms of a coherent risk measure. TVaR always satisfies sub-additivity; VaR does not.

See also: Coherent Risk Measure, TVaR, VaR

Discussed in: VaR vs. TVaR

Subject Loss

The loss stream entering a contract from the cedent’s book: everything the cedent presents, before any term applies. The contract’s own filter and contract period select the covered loss from it; the transforming terms (attachment, limit, cession rate) then produce the reinsurer’s 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, Gross Loss, Net Loss

Discussed in: Products and contracts

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.

Discussed in: Risk profiling

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: Products and contracts

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). With paid reinstatements, the premium and the expected reinstatement premium together cover these costs, and $K$ is measured on the outcome net of the reinstatement premium.

Discussed in: Standalone program pricing

Term (Financial Term)

A self-contained transformation of loss data, the atomic unit of a contract’s definition: it takes a YELT and produces a YELT, with no side effects and no state carried between trials. State inside a trial is allowed; the aggregate excess keeps a running total in claims order. The catalog holds the loss filter, contract period, scaling, occurrence excess, and aggregate excess, and terms combine into compositions.

Also known as: building block (informal)

See also: Composition, Contract

Discussed in: Contracts as compositions

TIV (Total Insured Value)

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

Discussed in: The trial worldview, Risk profiling

Top & Drop

A program structure where a single block of limit responds at a higher 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.⁷ It is a relationship between layers, the third besides inuring and 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 names it and does not model it.

See also: Program, Inuring, Forwarding, Layer

Discussed in: Programs

Tower

The stack of excess-of-loss layers placed on one shared exposure, each attaching where the one below exhausts. The ordinary shape of a program: in a vanilla tower the layers evaluate independently of one another, and only inuring or forwarding makes one layer’s result depend on another’s.

See also: Layer, Program, Inuring

Discussed in: Programs

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 YELT. 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.

See also: YELT, Event, Occurrence

Discussed in: The trial worldview

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

TVaR (Tail Value at Risk)

The average loss in the worst trials, at and beyond the VaR 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.

Also known as: CTE, ES (the three coincide for continuous distributions)

See also: VaR, Co-TVaR, Window TVaR, Capital Requirement

Discussed in: Tail Value at Risk

U

Underwriting Cycle

The insurance-economics literature’s name for the market cycle. It does not name the steps a single contract goes through; those are the underwriting workflow.

Underwriting Workflow

The sequence of steps a reinsurer takes one contract through: 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. For business that renews, it repeats with each renewal cycle.

Discussed in: Personas

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. Like risks attaching, it needs a policy inception date a YELT row does not carry.

See also: Losses Occurring, Risks Attaching

Discussed in: Contract period

Unexpected Loss

The amount by which a tail loss exceeds the expected loss; on this site, the 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, EP Curve, Return Period, Coherent Risk Measure

Discussed in: Value at Risk

Vendor Model

A 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

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 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, VaR, EP Curve

Discussed in: Additional metrics

Y

YELT (Year Event Loss Table)

The fundamental table of catastrophe risk analytics: one row per occurrence loss within a simulated 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). 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, YLT, Trial, Occurrence, Sign Convention

Discussed in: Personas (conceptual), The trial worldview (formal)

YLT (Year Loss Table)

A YELT reduced to trial resolution: one row per trial with columns (trial_id, loss), the occurrence detail dropped. A trial-level roll-up produces a YLT; it supports AEP metrics but not OEP metrics or occurrence-term evaluation. The reduction is lossy, irreversible, and always a chosen one: no financial term outputs a YLT; the aggregate excess stays at YELT resolution by erosion attribution. The “Y” carries the same caveat as the YELT’s: rows are trials, not calendar years.

See also: YELT, Roll-up, Trial

Discussed in: Portfolios

David R. Clark, “Basics of Reinsurance Pricing”, 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. ↩
Alexander Braun and Carolyn Kousky, Catastrophe Bonds, 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. ↩
Guy Carpenter, Glossary of Reinsurance Terms, 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 (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, 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. ↩
NAIC, Glossary of 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. ↩
Gary G. Venter, John A. Major, and Rodney E. Kreps, “Marginal Decomposition of Risk Measures”, 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 is the Euler component the incremental approach yields. John A. Major and Stephen J. Mildenhall, Introduction to Capital Modeling and Portfolio Management, 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. ↩
United Property & Casualty Insurance Company, “Second Event Property Catastrophe Excess of Loss Reinsurance Contract”, 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”, 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. ↩
Ivelin Zvezdov, “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”. ↩