Average Annual Loss Estimation

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.