Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics...

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...

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics...

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...

In the recent actuarial literature, several proofs have been given for the fact that if a random vector (XI, X2, ..., X~) with given marginals has a comonotonic joint distribution, the sum XI + X2 + ...+ Xn is the largest possible in convex order...

This paper presents a new axiomatic characterization of risk measures that are additive for independent random variables. In contrast to previous work, we include an axiom that guarantees monotonicity of the risk measure. Furthermore, the axiom of additivity for independent random variables is...