Порівняння методів

	Average Annual Loss Estimation	Probable Maximum Loss Estimation
Галузь	Disaster Studies	Disaster Studies
Родина	Process / pipeline	Process / pipeline
Рік появи	2005	2005
Автор методу	Patricia Grossi & Howard Kunreuther; Vitor Silva et al. (GEM)	Patricia Grossi & Howard Kunreuther; Kirsten Mitchell-Wallace et al.
Тип	Expected-value risk metric computed from a loss exceedance distribution	Tail (return-period) loss metric read from a loss exceedance distribution
Основоположне джерело	Grossi, P., & Kunreuther, H. (Eds.) (2005). Catastrophe Modeling: A New Approach to Managing Risk. Springer. ISBN: 9780387241050	Grossi, P., & Kunreuther, H. (Eds.) (2005). Catastrophe Modeling: A New Approach to Managing Risk. Springer. ISBN: 9780387241050
Інші назви	Annual Average Loss (AAL), Annualized Expected Loss, Pure Premium Estimation, Expected Annual Damage	Probable Maximum Loss (PML), Return-Period Loss, Tail Loss Estimation, Catastrophe Value-at-Risk
Пов'язані	4	4
Підсумок	Average annual loss (AAL) estimation computes the expected loss per year from a hazard, the long-run mean of annual losses obtained by weighting every possible event's loss by its annual frequency. It is the single most important summary statistic produced by probabilistic risk and catastrophe models, equal both to the frequency-weighted sum of event losses and to the area under the loss exceedance curve. Patricia Grossi and Howard Kunreuther's 2005 volume sets out how AAL and the exceedance curve are derived and used in risk management, and Vitor Silva and colleagues' 2020 global seismic risk model reports AAL (and AAL ratios) as its headline risk metric across the world. Because it is an expected value, AAL is additive across assets, perils, and regions, which makes it ideal for ranking risk, setting the technical (pure) insurance premium, and screening mitigation. Unlike return-period losses it says nothing about the tail, so it is the complement to probable maximum loss rather than a substitute. Estimating it correctly means handling both frequencies and the full range of event losses, including rare severe ones.	Probable maximum loss (PML) estimation reads a tail loss, the loss associated with a chosen rare return period or exceedance probability, from the loss exceedance curve produced by a probabilistic risk or catastrophe model. Where average annual loss summarizes the mean of the loss distribution, PML characterizes its extreme: a 1-in-250-year PML is the loss level exceeded with one percent probability in a year (a 0.4 percent probability for 1-in-250). Patricia Grossi and Howard Kunreuther's 2005 volume sets out PML and the exceedance-probability curve as core catastrophe-model outputs, and Kirsten Mitchell-Wallace and colleagues' 2017 practitioner's guide details how the industry computes and uses PML, including the crucial distinction between occurrence and aggregate exceedance. PML is the metric that drives solvency capital, reinsurance purchase, risk appetite, and regulatory stress tests, because catastrophe risk is about surviving the rare bad year, not the average one. It is a percentile (value-at-risk) of the loss distribution and therefore inherits both the power and the fragility of tail estimation. Defining it precisely, return period, occurrence versus aggregate, and uncertainty, is essential to using it responsibly.