Extreme M-quantiles as risk measures: From L1 to Lp optimization

Abstract : 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 p\in[1,2]. In this paper, 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 in a dependence framework motivated by financial and actuarial applications, before extrapolating these estimates to the very far tails. We also investigate the potential of extreme Lp quantiles as a tool for estimating the usual quantiles and expectiles themselves. We show the usefulness of extreme Lp quantiles and elaborate the choice of p through applications to some simulated and financial real data.
Type de document :
Article dans une revue
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2018
Liste complète des métadonnées

Littérature citée [7 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01585215
Contributeur : Stephane Girard <>
Soumis le : lundi 11 septembre 2017 - 12:42:52
Dernière modification le : mercredi 7 novembre 2018 - 01:16:18
Document(s) archivé(s) le : mardi 12 décembre 2017 - 19:05:20

Identifiants

  • HAL Id : hal-01585215, version 1

Collections

Citation

Abdelaati Daouia, Stéphane Girard, Gilles Stupfler. Extreme M-quantiles as risk measures: From L1 to Lp optimization. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2018. 〈hal-01585215〉

Partager

Métriques

Consultations de la notice

476

Téléchargements de fichiers

185