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Comonotonic Measures of Multivariate Risks

Mathematical Finance, Forthcoming

33 Pages Posted: 2 Apr 2008 Last revised: 7 Mar 2011

Ivar Ekeland

University of British Columbia (UBC) - Faculty of Education; Université Paris Dauphine - CEREMADE

Alfred Galichon

NYU, Department of Economics and Courant Institute

Marc Henry

Pennsylvania State University

Multiple version iconThere are 2 versions of this paper

Date Written: November 2, 2009

Abstract

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

Ekeland, Ivar and Galichon, Alfred and Henry, Marc, Comonotonic Measures of Multivariate Risks (November 2, 2009). Mathematical Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1115729 or http://dx.doi.org/10.2139/ssrn.1115729

Ivar Ekeland

University of British Columbia (UBC) - Faculty of Education ( email )

Université Paris Dauphine - CEREMADE ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Alfred Galichon (Contact Author)

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Marc Henry

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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