SOA Exam FAM Glossary: 25 Key Terms, Free (2026)

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Aggregate Loss Model: An aggregate loss model represents total claims in a period as the sum of N individual claim amounts, where N is the claim count (frequency) and each amount is drawn from a severity distribution. The compound distribution links frequency and severity.

Bornhuetter-Ferguson Method: The Bornhuetter-Ferguson method blends a chain-ladder estimate with an a-priori expected loss ratio. It places more weight on the a-priori for less mature accident years and more on chain-ladder development as years mature.
Buhlmann Credibility: Buhlmann credibility is the canonical greatest-accuracy framework. Credibility Z is the ratio of experience variance to total variance, with Z increasing in the number of exposures and decreasing in the variance of hypothetical means. $Z = \frac{n}{n + k}, \, k = \frac{E[\text{process variance}]}{\text{Var(hypothetical means)}}$

Chain-Ladder Method: The chain-ladder method projects ultimate losses by applying age-to-age development factors derived from historical loss triangles. It assumes future development resembles past development by accident year.
Coinsurance: Coinsurance is a policy provision requiring the insured to share losses with the insurer above a deductible up to a coverage limit. It mitigates moral hazard and aligns the insured's incentives with claim-cost management.
Compound Distribution: A compound distribution describes the aggregate of a random number of random claim amounts. The mean is the product of the frequency mean and the severity mean under independence; the variance combines both sources.
Conditional Tail Expectation (CTE): CTE is the expected loss given that the loss exceeds the value-at-risk threshold at a specified confidence level. Also called expected shortfall, CTE is coherent (sub-additive) while VaR is not. $CTE_\alpha = E[X \mid X > VaR_\alpha]$
Credibility Theory: Credibility theory is the framework for blending experience data with a base rate. The credibility factor Z weights actual experience against the prior expectation; classical credibility uses Z = sqrt(n/n_full), Buhlmann uses the variance-based formula.

Deductible: A deductible is the amount the insured pays out of pocket before the insurer's coverage attaches. It reduces moral hazard, eliminates small-claim friction, and serves as a tool for risk-sharing and premium reduction.

Exposure to Loss: Exposure to loss is a measure of the volume of risk under coverage, expressed in vehicle-years, payroll, sales, square feet, or other appropriate base. It is the denominator in pure-premium ratemaking.

Force of Mortality: The force of mortality μ(x) is the instantaneous death rate at age x. It equals the limit of the conditional probability of death in a small interval divided by the interval length and underlies modern life-contingencies modeling. $\mu_x = -\frac{d}{dx} \ln S(x)$
Frequency Distribution: A frequency distribution is the probability distribution of the number of claims in a period. Common families include Poisson (no overdispersion), binomial (fixed N), and negative binomial (allows overdispersion via gamma-mixed Poisson).

Increased Limits Factor (ILF): An increased-limits factor is the ratio of expected loss at a higher policy limit to expected loss at a base limit. ILFs are used to price higher limits relative to a base rate while preserving consistency across limit options.

Layer of Loss: A layer of loss is the portion of a loss between two attachment points (for example $1 million excess of $1 million). Reinsurance contracts and excess policies attach on specific layers, and layer pricing depends on the conditional severity within the layer.
Loss Development Factor (LDF): A loss development factor (LDF) is the ratio used to project losses from one stage of maturity to the next. LDFs are typically estimated from historical loss triangles and combined to produce age-to-ultimate factors.
Loss Ratio: The loss ratio is the ratio of incurred losses to earned premium. It is the primary measure of insurance underwriting profitability before accounting for expenses.
Loss Reserves: Loss reserves are the estimated liability for losses that have occurred but have not been paid. They include case reserves for known claims and incurred-but-not-reported (IBNR) reserves for the unreported portion.

Maximum Likelihood Estimation (MLE): Maximum likelihood estimation chooses parameters of a distribution to maximize the likelihood (or log-likelihood) of the observed data. It is broadly used in fitting severity and frequency models and has desirable asymptotic properties (consistency, efficiency, normality).
Mixed Poisson Distribution: A mixed Poisson distribution arises when the Poisson rate parameter is itself random. It produces overdispersion relative to the pure Poisson and includes the negative binomial as a gamma-mixed Poisson.

Pure Premium: Pure premium is the expected loss per exposure unit. It is the loss component of the gross premium before expense, profit, and contingency loadings, and is the central quantity in exposure-based ratemaking.

Reserving (Loss): Reserving is the process of estimating liabilities for losses that have occurred but have not yet been paid or even reported. Common methods include chain-ladder, Bornhuetter-Ferguson, and expected-loss-ratio approaches.

Severity Distribution: A severity distribution is the probability distribution of individual claim amounts. Common families include exponential, gamma, Pareto, lognormal, and Weibull, with heavier-tailed distributions appropriate when extreme claims are material.
Stop-Loss Reinsurance: Stop-loss reinsurance pays once the cedant's aggregate losses in a period exceed a retention. It is aggregate excess coverage that protects against accident-year volatility.

Tail-Value-at-Risk (TVaR): Tail-value-at-risk is the average of losses above the VaR threshold. It is a coherent risk measure (unlike VaR) and captures the severity of tail events.

Value-at-Risk (VaR): Value-at-risk at confidence α is the quantile of the loss distribution at that confidence level: with probability α, losses will not exceed VaR. It is widely used in regulatory frameworks despite not being sub-additive.