Comonotonic measures of multivariate risks
Ekeland, Ivar; Galichon, Alfred; Henry, Marc (2012), Comonotonic measures of multivariate risks, Mathematical Finance, 22, 1, p. 109–132. 10.1111/j.1467-9965.2010.00453.x
TypeArticle accepté pour publication ou publié
Journal nameMathematical Finance
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Départment de sciences économiques
Abstract (EN)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.
Subjects / Keywordsstrongly coherent risk measures; optimal transportation; maximal correlation; comonotonicity; coherent risk measures; regular risk measures
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