Robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance when making well-informed risk management decisions. In this paper, we quantify for any given distortion risk measure its robustness to distributional uncertainty by...

Existing risk capital allocation methods, such as the Euler rule, work under the explicit assumption that portfolios are formed as linear combinations of random loss/profit variables, with the firm being able to choose the portfolio weights. This assumption is unrealistic in an insurance...

We show that maximizing distortion risk measures over the set of distribution functions with given mean is equivalent to maximizing their concave counterpart. In the case of Value-at-Risk and Tail Value-at-Risk the equivalence also holds when adding information on higher moments