Dual theory of choice with multivariate risks
We propose a multivariate extension of Yaariʼs 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 using 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.
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- Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
- François Bourguignon & Satya Chakravarty, 2003.
"The Measurement of Multidimensional Poverty,"
Journal of Economic Inequality,
Springer, vol. 1(1), pages 25-49, April.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- Zephyr, 2010. "The city," City, Taylor & Francis Journals, vol. 14(1-2), pages 154-155, February.
- Thibault Gajdos & John Weymark, 2005.
"Multidimensional generalized Gini indices,"
Springer, vol. 26(3), pages 471-496, October.
- Thibault Gajdos & John A. Weymark, 2003. "Multidimensional generalized Gini indices," ICER Working Papers - Applied Mathematics Series 16-2003, ICER - International Centre for Economic Research.
- Thibault Gajdos & John A. Weymark, 2003. "Multidimensional Generalized Gini Indices," Vanderbilt University Department of Economics Working Papers 0311, Vanderbilt University Department of Economics, revised Jul 2003.
- Thibault Gadjos & John A, Weymark, 2003. "Multidimensional Generalized Gini Indices," Working Papers 2003-16, Centre de Recherche en Economie et Statistique.
- Thibault Gajdos & John Weymark, 2005. "Multidimensional Generalized Gini Indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085881, HAL.
- Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
- Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
- Tsui Kai-Yuen, 1995. "Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The Atkinson-Kolm-Sen Approach," Journal of Economic Theory, Elsevier, vol. 67(1), pages 251-265, October.
- Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
- Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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