Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions

Abstract

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2014.html Chapitre dans "Future Perspectives in Risk Models and Finance", eds. A. Bensoussan, D. Guegan, C. Tapiero, Volume 211 of the series International Series in Operations Research & Management Science, 89-124, 2015Documents de travail du Centre d'Economie de la Sorbonne 2014.08 - ISSN : 1955-611XThe particular subject of this paper, is to construct a general framework that can consider and analyse in the same time upside and downside risks. This paper offers a comparative analysis of concept risk measures, we focus on quantile based risk measure (ES and VaR), spectral risk measure and distortion risk measure. After introducing each measure, we investigate their interest and limit. Knowing that quantile based risk measure cannot capture correctly the risk aversion of risk manager and spectral risk measure can be inconsistent to risk aversion, we propose and develop a new distortion risk measure extending the work of Wang (2000) [38] and Sereda et al (2010) [34]. Finally, we provide a comprehensive analysis of the feasibility of this approach using the S&P500 data set from o1/01/1999 to 31/12/2011.Ce papier propose un cadre général qui permet d'analyser dans le même temps les risques à la hausse et la baisse. Après une revue (avec limites et intérêt) sur les mesures de risques classiques : VaR, ES et mesure spectrale, nous proposons et développons une nouvelle mesure du risque appeler mesure de distorsion qui étend le travail de Wang (2000) et Sereda et al (2010) pour des distributions bimodales et multimodales