Extreme versions of Wang risk measures and their estimation

Gilles Stupfler (1) , Jonathan El Methni (2)

1 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Among the many possible ways to study the behavior of a real-valued random variable in its right tail, a particularly general one is given by considering the family of its Wang distortion risk measures. This class of risk measures encompasses various interesting risk measures, 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. Special cases of the risk measures of interest include the extreme Value-at-Risk, extreme Tail-Value-at-Risk as well as the recently introduced extreme Conditional Tail Moment. We then introduce adapted estimators and give 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.

Mots clés: Wang distortion risk measure; conditional tail moment; heavy-tailed distribution.

Domaines: Statistiques [math.ST]

Gilles Stupfler, Jonathan El Methni. Extreme versions of Wang risk measures and their estimation. The 9th international conference on Extreme Value Analysis, Jun 2015, Ann Arbor, United States. ⟨hal-01169904⟩