Extreme versions of Wang risk measures and their estimation for heavy-tailed distributions

Abstract

Among the many possible ways to study the right tail of a real-valued random variable, a particularly general one is given by considering the family of its Wang distortion risk measures. This class of risk measures encompasses various interesting indicators, such as the widely used Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR). In this paper, we first build simple extreme analogues of Wang distortion risk measures. We then introduce adapted estimators when the random variable of interest has a heavy-tailed distribution and we prove their asymptotic normality. The finite sample performance of our estimators is assessed on a simulation study and we showcase our technique on a set of real data.