In this paper we examine and summarize properties of several well-known risk measuresthat can be used in the framework of setting solvency capital requirements for a risky business.Special attention is given to the class of (concave) distortion risk measures. We investigatethe relationship...

This article gives counterexamples for some conjecturesabout risk orders. One is that in risky situations, diversificationis always beneficial. A counterexample is providedby the Cauchy distribution, for which the sample means havethe same distribution as the sample elements, meaning that...