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Dual theory of choice with multivariate risks

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Document pages: 22 pages

Abstract: We propose a multivariate extension of Yaari s dual theory of choice underrisk. We show that a decision maker with a preference relation onmultidimensional prospects that preserves first order stochastic dominance andsatisfies comonotonic independence behaves as if evaluating prospects using aweighted sum of quantiles. Both the notions of quantiles and of comonotonicityare extended to the multivariate framework using optimal transportation maps.Finally, risk averse decision makers are characterized within this frameworkand their local utility functions are derived. Applications to the measurementof multi-attribute inequality are also discussed.

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