Abstract: In this paper, we build simple extreme analogues of Wang distortion risk measures and we show how this makes it possible to consider many standard measures of extreme risk, including the usual extreme Value-at-Risk or Tail-Valueat- Risk, as well as the recently introduced extreme Conditional Tail Moment, in a unified framework. 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 in a simulation study and we showcase our techniques on two sets of data.

Key words and phrases: Asymptotic normality, conditional tail moment, distortion risk measure, extreme-value statistics, heavy-tailed distribution.