Comonotonic Measures of Multivariate Risks
Mathematical Finance, Forthcoming
33 Pages Posted: 2 Apr 2008 Last revised: 7 Mar 2011
Date Written: November 2, 2009
We propose a multivariate extension of a well-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 fonctions. 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.
Keywords: regular risk measures, coherent risk
JEL Classification: D81, C61
Suggested Citation: Suggested Citation