Aggregate exceedance probability curve

An aggregate exceedance probability curve associates with each amount the probability that the sum of all events in a year exceeds it. It is the reference quantity for sizing an aggregate cover, calibrating an annual deductible and estimating the capital catastrophe losses require over one year. The problem it solves is frequency, which the occurrence curve ignores by construction: a portfolio suffering six medium windstorms in a year appears nowhere on an occurrence curve, yet may cost more than one large event. The gap between the two curves at equal return period therefore measures directly the weight of frequency in the risk profile. A narrow gap signals a portfolio dominated by a single extreme peril, a wide gap a portfolio exposed to the accumulation of medium events, and the reinsurance program to build is not the same in the two cases. Prudential regimes generally reason on an aggregate basis.

For the same French cedant in 2026, the aggregate curve gives 149 million euros at one hundred years and 214 million at two hundred years, against 118 and 172 million on the occurrence curve. The 42 million gap at two hundred years measures frequency's contribution, and justifies buying a 45 million xs 60 aggregate cover that examining the occurrence curve alone would never have suggested.

AEP curve, Courbe AEP, Aggregate exceedance probability, Courbe de dépassement cumulée