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...

In this paper we review existing statistical measures for systemic risk and discuss their strengths and weaknesses. Among them we discuss the Conditional Value-at-Risk (CoVaR) introduced by Adrian and Brunnermeier (2010) and the Systemic Expected Shortfall (SES) of Acharya, Pedersen, Philippon...

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