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...

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...

We propose an optimization approach to allocating economic capital, distinguishing between an allocation or raising principle and a measure for the risk residual. The approach is applied both at the aggregate (conglomerate) level and at the individual (subsidiary) level and yields an integrated...

In this paper we analyze and evaluate a standard approach financial institutions use to calculate their so-called total economic capital. If we consider a business that faces a total random loss S over a given one-year horizon then economic capital is traditionally defined as the difference...

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...

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...