Posted: 21 Jan 2012
Date Written: January 2012
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 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.
Keywords: regular risk measures, coherent risk measures, comonotonicity, maximal correlation, optimal transportation, strongly coherent risk measures
Suggested Citation: Suggested Citation
Ekeland, Ivar and Galichon, Alfred and Henry, Marc, Comonotonic Measures of Multivariate Risks (January 2012). Mathematical Finance, Vol. 22, Issue 1, pp. 109-132, 2012. Available at SSRN: https://ssrn.com/abstract=1989280 or http://dx.doi.org/10.1111/j.1467-9965.2010.00453.x
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