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Dual theory of choice with multivariate risks

Author

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  • Galichon, Alfred
  • Henry, Marc

Abstract

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.

Suggested Citation

  • Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1501-1516 DOI: 10.1016/j.jet.2011.06.002
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    References listed on IDEAS

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    1. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 471-496.
    4. 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.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    6. 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.
    7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    8. François Bourguignon & Satya Chakravarty, 2003. "The Measurement of Multidimensional Poverty," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 25-49, April.
    9. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    11. Zephyr, 2010. "The city," City, Taylor & Francis Journals, vol. 14(1-2), pages 154-155, February.
    12. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, Oxford University Press, vol. 91(1), pages 1-13.
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    Citations

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    Cited by:

    1. Marcello Basili & Paulo Casaca & Alain Chateauneuf & Maurizio Franzini, 2017. "Multidimensional Pigou–Dalton transfers and social evaluation functions," Theory and Decision, Springer, pages 573-590.
    2. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    3. Matteo Del Vigna, 2012. "Stochastic dominance for law invariant preferences: The happy story of elliptical distributions," Working Papers - Mathematical Economics 2012-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    4. Sinem Bas & Philippe Bich & Alain Chateauneuf, 2016. "Multidimensional inequalities and generalized quantile functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01313118, HAL.
    5. repec:hal:wpaper:hal-01313118 is not listed on IDEAS
    6. Elisa Pagani, 2015. "Certainty Equivalent: Many Meanings of a Mean," Working Papers 24/2015, University of Verona, Department of Economics.
    7. repec:eee:jmvana:v:161:y:2017:i:c:p:96-102 is not listed on IDEAS

    More about this item

    Keywords

    Risk; Rank dependent utility theory; Multivariate comonotonicity; Optimal transportation; Multi-attribute inequality; Gini evaluation functions;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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