Conditional value‐at‐risk bounds for compound Poisson risks and anormal approximation

Abstract

A considerable number of equivalent formulas defining conditional value‐at‐risk and expected shortfall are gathered together. Then we present a simple method to bound the conditional value‐at‐risk of compound Poisson loss distributions under incomplete information about its severity distribution, which is assumed to have a known finite range, mean, and variance. This important class of nonnormal loss distributions finds applications in actuarial science, where it is able to model the aggregate claims of an insurance‐risk business.

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