Abstract

https://ssrn.com/abstract=1115729
 
 

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Comonotonic Measures of Multivariate Risks


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

November 2, 2009

Mathematical Finance, Forthcoming

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.

Number of Pages in PDF File: 33

Keywords: regular risk measures, coherent risk

JEL Classification: D81, C61


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Date posted: April 2, 2008 ; Last revised: March 7, 2011

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

Contact Information

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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