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...

We consider a continuous-time Markowitz type portfolio problem that consists of minimizing the discounted cost of a given cash-fl ow under the constraint of a restricted Capital at Risk. In a Black-Scholes setting, upper and lower bounds are obtained by means of simple analytical expressions...

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...