Risk measures and benchmark distributions Abstract
In this talk we discuss how the commonly used risk measures fail to control the probability of exceeding given level of losses. In order to address this aspect of tail risk we propose new classes of law invariant risk measures that generalize Value at Risk and Expected Shortfall. The key ingredient is a benchmark function which allows to specify admissibility constraints based on the whole tail of the distribution. As an interesting particular case, stochastic dominance constraints can be used in order to define acceptability. We present the main finance theoretical and statistical properties of this new class of risk measures and for the convex case we show its dual representation. Merits and drawbacks are discussed and applications to capital adequacy, portfolio risk management and catastrophic risk are presented. Based on joint works with Cosimo Munari, Valeria Bignozzi and Ruodu Wang.