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

  • Dominique Guégan
  • Bertrand Hassani
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 211)


The particular subject of this paper, is to construct a general framework that can consider and analyse in the same time the 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 (J Risk Insurance 67, 2000) and Sereda et al. (Handbook of Portfolio Construction 2012). Finally we provide a comprehensive analysis of the feasibility of this approach using the S&P500 data set from 01/01/1999 to 31/12/2011.


Saddle Point Risk Aversion Risk Measure Distortion Function Downside Risk 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University Paris 1 Panthéon-Sorbonne et New York University Polytechnic School of EngineeringBrooklynUSA
  2. 2.University Paris 1 Panthéon-SorbonneParis Cedex 13France
  3. 3.Paris Cedex 13France

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