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Comonotonic measures of multivariates risks

  • Alfred Galichon

    (Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X)

  • Ivar Ekeland

    (Canada Research Chair in Mathematical Economics - University of British Columbia)

  • Marc Henry

    (Départment de sciences économiques - Université de Montréal, CIRANO - Montréal, CIREQ - Centre Interuniversitaire de Recherche en Economie Quantitative)

We propose a multivariate extension of a well-known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors through generalized quantile functions. Moreover, we propose to replace the current law invari- ance, subadditivity and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural economic interpretation. Finally, we refor- mulate the computation of regular and coherent risk measures as an optimal transportation problem, for which we provide an algorithm and implementation.

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Paper provided by HAL in its series Working Papers with number hal-00401828.

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Date of creation: 06 Jul 2009
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Handle: RePEc:hal:wpaper:hal-00401828
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  1. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, 04.
  2. Elyès Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued Coherent Risk Measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00167154, HAL.
  3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  5. Touzi, Nizar & Schachermayer, Walter & Jouini, Elyès, 2006. "Law Invariant Risk Measures Have the Fatou Property," Economics Papers from University Paris Dauphine 123456789/342, Paris Dauphine University.
  6. Rüschendorf Ludger, 2006. "Law invariant convex risk measures for portfolio vectors," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 12, July.
  7. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
  8. Touzi, Nizar & Meddeb, Moncef & Jouini, Elyès, 2004. "Vector-valued Coherent Risk Measures," Economics Papers from University Paris Dauphine 123456789/353, Paris Dauphine University.
  9. Burgert, Christian & Ruschendorf, Ludger, 2006. "Consistent risk measures for portfolio vectors," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 289-297, April.
  10. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
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