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Événements et séminaires - LSTA
Laboratoire de Statistique Théorique et Appliquée

Partenariats

23/05/2017 - Stéphane Girard (INRIA, Grenoble)

 Groupe de travail théorie des valeurs extrêmes

Estimation de mesures de risques à partir des Lp-quantiles extrêmes

collaboration avec Abdelaati DAOUIA (Toulouse School of Economics) & Gilles STUPFLER (University of Nottingham)

 

The class of quantiles lies at the heart of extreme-value theory and is one of the basic tools in risk management. The alternative family of expectiles is based on squared rather than absolute error loss minimization. It has recently been receiving a lot of attention in actuarial science, econometrics and statistical finance. Both quantiles and expectiles can be embedded in a more general class of M-quantiles by means of Lp optimization. These generalized Lp-quantiles steer an advantageous middle course 
between ordinary quantiles and expectiles without sacrificing their virtues too much for 1<p<2. In this talk, we investigate their estimation from the perspective of extreme values in the class of heavy-tailed distributions. We construct estimators of the intermediate Lp-quantiles and establish their asymptotic normality before extrapolating these estimates to the tails. Some illustrations on simulated and real data are provided.