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Dual Theory of Choice Under Multivariate Risks

22 Pages Posted: 29 Apr 2008 Last revised: 7 Oct 2011

Alfred Galichon

NYU, Department of Economics and Courant Institute

Marc Henry

Pennsylvania State University

Date Written: February 23, 2010

Abstract

We propose a multivariate extension of Yaari's dual theory of choice under risk. We show that a decision maker with a preference relation on multidimensional prospects that preserves first order stochastic dominance and satisfies comonotonic independence behaves as if evaluating prospects with a weighted sum of quantiles. Both the notions of quantiles and of comonotonicity are extended to the multivariate framework using optimal transportation maps. Finally, risk averse decision makers are characterized within this framework and their local utility functions are derived. Applications to the measurement of multi-attribute inequality are also discussed.

Keywords: risk, non-expected utility theory, comonotonicity, optimal transportation

JEL Classification: D81, C61

Suggested Citation

Galichon, Alfred and Henry, Marc, Dual Theory of Choice Under Multivariate Risks (February 23, 2010). Journal of Economic Theory, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1126483

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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