Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions

Abstract : A general way to study the extremes of a random variable is to consider the family of its Wang distortion risk measures. This class of risk measures encompasses several popular indicators such as the classical quantile/Value-at-Risk, the Tail-Value-at-Risk and the recently introduced Conditional Tail Moments, among others. A couple of very recent studies have focused on the estimation of extreme analogues of such quantities. In this paper, we consider trimmed and winsorised versions of the empirical counterparts of extreme Wang distortion risk measures. We analyse their asymptotic properties, and we show that we can construct bias-corrected trimmed or winsorised estimators of extreme Wang distortion risk measures who appear to perform overall better than their standard empirical counterparts in practice when the underlying distribution has a very heavy right tail. We also showcase our technique on a set of real fire insurance data.
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Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01406342
Contributeur : Jonathan El Methni <>
Soumis le : mardi 7 mars 2017 - 14:11:25
Dernière modification le : dimanche 12 mars 2017 - 01:05:20

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  • HAL Id : hal-01406342, version 2

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Jonathan El Methni, Gilles Stupfler. Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions. 2016. <hal-01406342v2>

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