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📉 '''Loss distribution''' is a statistical representation of the probability and magnitude of [[Definition:Insurance claim | losses]] that an [[Definition:Insurance carrier | insurer]] or portfolio may experience over a defined period. Rather than viewing losses as a single expected number, a loss distribution captures the full range of outcomes — from frequent, low-severity claims to rare, catastrophic events — and assigns a probability to each. It serves as the mathematical backbone of [[Definition:Actuarial science | actuarial]] pricing, [[Definition:Loss reserving | reserving]], and [[Definition:Capital modeling | capital modeling]] across virtually every [[Definition:Line of business | line of business]].

🔬 Actuaries construct loss distributions by fitting historical claims data to parametric models — common choices include the [[Definition:Lognormal distribution | lognormal]], [[Definition:Pareto distribution | Pareto]], and [[Definition:Gamma distribution | gamma]] distributions for individual claim severity, and the [[Definition:Poisson distribution | Poisson]] or [[Definition:Negative binomial distribution | negative binomial]] for claim frequency. The aggregate loss distribution, which combines frequency and severity, is often generated through [[Definition:Monte Carlo simulation | Monte Carlo simulation]] or analytical convolution methods. In [[Definition:Catastrophe modeling | catastrophe modeling]], event-based simulations produce loss distributions for portfolios exposed to natural perils such as hurricanes and earthquakes, allowing insurers to estimate [[Definition:Probable maximum loss (PML) | probable maximum losses]] and set [[Definition:Reinsurance | reinsurance]] attachment points.

💡 A well-calibrated loss distribution underpins virtually every financial decision an insurer makes. [[Definition:Pricing | Pricing]] actuaries use it to set [[Definition:Premium | premiums]] that cover expected losses plus a margin for variability. [[Definition:Risk management | Risk managers]] and [[Definition:Chief risk officer (CRO) | chief risk officers]] rely on tail percentiles — such as the 99.5th percentile under [[Definition:Solvency II | Solvency II]] — to determine required [[Definition:Economic capital | economic capital]]. [[Definition:Reinsurance broker | Reinsurance brokers]] use loss distributions to structure programs that efficiently transfer tail risk while retaining profitable attritional layers. When the underlying distribution is misspecified — for example, by underweighting heavy tails in liability lines — the consequences ripple outward through inadequate rates, insufficient reserves, and capital shortfalls, underscoring why distribution selection and validation remain among the most consequential exercises in insurance analytics.

'''Related concepts'''
{{Div col|colwidth=20em}}
* [[Definition:Actuarial science]]
* [[Definition:Catastrophe modeling]]
* [[Definition:Monte Carlo simulation]]
* [[Definition:Probable maximum loss (PML)]]
* [[Definition:Aggregate loss]]
* [[Definition:Capital modeling]]
{{Div col end}}

Definition:Loss distribution - Revision history

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