Extreme versions of Wang risk measures and their estimation

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 and Tail Value-at-Risk, which are especially popular in actuarial science, for instance. In this communication, we first 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-Value-at-Risk, as well as the recently in- troduced 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 on a simulation study and we showcase our techniques on an actuarial data set.
Type de document :
Communication dans un congrès
Extremes, Copulas and Actuarial Sciences, Feb 2016, Marseille, France
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https://hal.archives-ouvertes.fr/hal-01313679
Contributeur : Jonathan El Methni <>
Soumis le : mardi 10 mai 2016 - 11:50:16
Dernière modification le : mardi 10 octobre 2017 - 11:22:04

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  • HAL Id : hal-01313679, version 1

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Jonathan El Methni, Gilles Stupfler. Extreme versions of Wang risk measures and their estimation. Extremes, Copulas and Actuarial Sciences, Feb 2016, Marseille, France. 〈hal-01313679〉

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