Transformation of Distributions, Robustness and Coherent Risk Measures

Groupe de Recherche sur le Risque l'Information et la Decision (GRID) Working Paper No. 17-2003

29 Pages Posted: 3 Nov 2003

See all articles by Michel Verlaine

Michel Verlaine

Ecole Nationale Superieure - ENSAM

Abstract

This paper discusses coherent risk measures and the transformation of so-called objective probability distributions, also called distortion functions. It is argued that observed probability weighting as described in Kahneman and Tversky (1992) is not due to behavioral (irrational ?) reasons, but can be explained by robust behavior when the probability kernel cannot uniquely be pinned down. S-shaped dostorion functions can then be recovered by maximum entropy techniques. Finally, it is argued that coherent risk measures can be derived from such a distortion. They are hence consistent with behavior under uncertainty (given a family of probability distributions). It becomes then possible to construct VaR measures calibrated for different profiles of costumers and use them for portfolio optimization.

JEL Classification: G11, D81

Suggested Citation

Verlaine, Michel, Transformation of Distributions, Robustness and Coherent Risk Measures. Groupe de Recherche sur le Risque l'Information et la Decision (GRID) Working Paper No. 17-2003, Available at SSRN: https://ssrn.com/abstract=458421 or http://dx.doi.org/10.2139/ssrn.458421

Michel Verlaine (Contact Author)

Ecole Nationale Superieure - ENSAM ( email )

F-75634 Paris Cedex 13
France

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