Comonotonic measures of multivariate risks

Ivar Ekeland (1) , Alfred Galichon (2) , Marc Henry (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 ECON - Département d'économie (Sciences Po)
3 Départment de sciences économiques

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.

Domains: Humanities and Social Sciences; Economics and Finance

Ivar Ekeland, Alfred Galichon, Marc Henry. Comonotonic measures of multivariate risks. Mathematical Finance, 2012, 22 (1), pp.109-132. ⟨10.1111/j.1467-9965.2010.00453.x⟩. ⟨hal-01053550⟩