Comonotonic measures of multivariate risks

Ivar Ekeland, Alfred Galichon, Marc Henry

    Research output: Contribution to journalArticlepeer-review


    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 invariance, subadditivity, and comonotonicity axioms by an equivalent property we callstrong coherenceand 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.

    Original languageEnglish (US)
    Pages (from-to)109-132
    Number of pages24
    JournalMathematical Finance
    Issue number1
    StatePublished - Jan 2012


    • Coherent risk measures
    • Comonotonicity
    • Maximal correlation
    • Optimal transportation
    • Regular risk measures
    • Strongly coherent risk measures

    ASJC Scopus subject areas

    • Accounting
    • Social Sciences (miscellaneous)
    • Finance
    • Economics and Econometrics
    • Applied Mathematics


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