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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

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Type
Article accepté pour publication ou publié
Date
2012
Journal name
Mathematical Finance
Volume
22
Number
1
Publisher
WIley
Pages
109–132
Publication identifier
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Author(s)
Ekeland, Ivar
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Galichon, Alfred

Henry, Marc
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 / Keywords
strongly coherent risk measures; optimal transportation; maximal correlation; comonotonicity; coherent risk measures; regular risk measures