Comonotonic measures of multivariate risks

Ivar Ekeland, Alfred Galichon, Marc Henry

    Research output: Contribution to journalArticle

    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 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
    Volume22
    Issue number1
    DOIs
    StatePublished - Jan 2012

    Fingerprint

    Comonotonicity
    Coherent Risk Measures
    Optimal Transportation
    Subadditivity
    Quantile Function
    Transportation Problem
    Invariance
    Random Vector
    Generalized Functions
    Axioms
    Economics
    interpretation
    Law
    economics
    Coherent risk measures
    Multivariate risk

    Keywords

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

    ASJC Scopus subject areas

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

    Cite this

    Comonotonic measures of multivariate risks. / Ekeland, Ivar; Galichon, Alfred; Henry, Marc.

    In: Mathematical Finance, Vol. 22, No. 1, 01.2012, p. 109-132.

    Research output: Contribution to journalArticle

    Ekeland, I, Galichon, A & Henry, M 2012, 'Comonotonic measures of multivariate risks', Mathematical Finance, vol. 22, no. 1, pp. 109-132. https://doi.org/10.1111/j.1467-9965.2010.00453.x
    Ekeland, Ivar ; Galichon, Alfred ; Henry, Marc. / Comonotonic measures of multivariate risks. In: Mathematical Finance. 2012 ; Vol. 22, No. 1. pp. 109-132.
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