Comonotonic Measures of Multivariate Risks
Ekeland, Ivar; Galichon, Alfred; Henry, Marc (2012), Comonotonic Measures of Multivariate Risks, Mathematical Finance, 22, 1, p. 109-132. http://dx.doi.org/10.1111/j.1467-9965.2010.00453.x
TypeArticle accepté pour publication ou publié
Journal nameMathematical Finance
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Abstract (EN)We propose a multivariate extension of a well-known characterization byS. Kusuoka of regular and coherent risk measures as maximal correlation functionals.This involves an extension of the notion of comonotonicity to random vectors throughgeneralized quantile functions. Moreover, we propose to replace the current law invari-ance, subadditivity and comonotonicity axioms by an equivalent property we call strongcoherence and that we argue has more natural economic interpretation. Finally, we refor-mulate the computation of regular and coherent risk measures as an optimal transportationproblem, for which we provide an algorithm and implementation.
Subjects / KeywordsOptimal Transportation; Maximal Correlation; Regular Risk Measures; Coherent Risk Measures; Comonotonicity
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