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Comonotonic measures of multivariates risks

Author

Listed:
  • Alfred Galichon

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Ivar Ekeland

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

  • Marc Henry

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

Abstract

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.

Suggested Citation

  • Alfred Galichon & Ivar Ekeland & Marc Henry, 2009. "Comonotonic measures of multivariates risks," Working Papers hal-00401828, HAL.
    • Handle: RePEc:hal:wpaper:hal-00401828
    Note: View the original document on HAL open archive server: https://hal.science/hal-00401828
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    strongly coherent risk measures.; regular risk measures; coherent risk measures; comonotonicity; maximal correlation; optimal transportation; strongly coherent risk measures;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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