Worst case risk measurement: Back to the future?

This paper studies the problem of finding best-possible upper bounds on a rich class of risk measures, expressible as integrals with respect to measures, under incomplete probabilistic information. Both univariate and multivariate risk measurement problems are considered. The extremal probability distributions, generating the worst case scenarios, are also identified.The problem of worst case risk measurement has been studied extensively by Etienne De Vijlder and his co-authors, within the framework of finite-dimensional convex analysis. This paper revisits and extends some of their results.

► We construct best-possible upper bounds on a rich class of risk measures. ► The worst case scenarios, attaining the upper bounds, are also identified. ► Some topical examples of risk measurement problems are studied in detail. ► We show that the approach can also be applied in a multivariate setting.