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

Linear GARCH(1,1) and GJR GARCH(1,1) processes are established as regularly varying, meaning their heavy tails follow a Power Law, under conditions that allow the innovations from the, respective, processes to be either symmetrically distributed or skewed. Skewness is considered a stylized fact...

Understanding and measuring model risk is important to financial practitioners. However, there lacks a non-parametric approach to model risk quantification in a dynamic setting and with path-dependent losses. We propose a complete theory generalizing the relative-entropic approach by Glasserman...

Weekly, quarterly and yearly risk measures are crucial for risk reporting according to Basel III and Solvency II. For the respective data frequencies, the authors show in a simulation and back-test study that available data series are not sufficient in order to estimate Value at Risk and...