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Comonotonic measures of multivariate risks

Author

Listed:
  • Ivar Ekeland

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Alfred Galichon

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Marc Henry

    (Départment de sciences économiques - UdeM - Université de Montréal)

Abstract

We propose amultivariate extension of awell-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 invariance, subadditivity, and comonotonicity axioms by an equivalent property we call strong coherence and that we argue has more natural economic interpretation. Finally, we reformulate the computation of regular and coherent risk measures as an optimal transportation problem, for which we provide an algorithm and implementation.

Suggested Citation

  • Ivar Ekeland & Alfred Galichon & Marc Henry, 2012. "Comonotonic measures of multivariate risks," Post-Print hal-01053550, HAL.
    • Handle: RePEc:hal:journl:hal-01053550
    DOI: 10.1111/j.1467-9965.2010.00453.x
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01053550
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    References listed on IDEAS

    as
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    More about this item

    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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