Dual Theory of Choice Under Multivariate Risks
22 Pages Posted: 29 Apr 2008 Last revised: 7 Oct 2011
Date Written: February 23, 2010
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
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