Comonotonic measures of multivariate risks

Ivar Ekeland, Alfred Galichon (alfred.galichon@gmail.com) and Marc Henry
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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

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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.

Date: 2012
Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01053550v1
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Published in Mathematical Finance, 2012, 22 (1), pp.109-132. ⟨10.1111/j.1467-9965.2010.00453.x⟩

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Related works:
Working Paper: Comonotonic measures of multivariate risks (2021)
Working Paper: Comonotonic measures of multivariate risks (2012)
Working Paper: Comonotonic measures of multivariates risks (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:spmain:hal-01053550

DOI: 10.1111/j.1467-9965.2010.00453.x

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