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Generalized Expected Utility Analysis of Multivariate Risk Aversion

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  • Karni, Edi

Abstract

This paper extends M. J. Machina's generalized expected utility analysis to preferences over multivariate distributions. Within the extended framework, the relation "more risk averse than" is defined, characterized, and applied to the analysis of consumption-saving decisions under risk. The notion of decreasing risk aversion is also characterized. The paper shows that standard results obtained within the framework of expected utility theory can be extended if the restrictions imposed on the utility function in expected utility theory are imposed on the local utility functions in Machina's theory. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

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  • Karni, Edi, 1989. "Generalized Expected Utility Analysis of Multivariate Risk Aversion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(2), pages 297-305, May.
    • Handle: RePEc:ier:iecrev:v:30:y:1989:i:2:p:297-305
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    References listed on IDEAS

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    1. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    4. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    5. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    6. Allen, Beth, 1987. "Smooth preferences and the approximate expected utility hypothesis," Journal of Economic Theory, Elsevier, vol. 41(2), pages 340-355, April.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    8. Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 293-317, December.
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    Cited by:

    1. Colson, Gérard, 1993. "Prenons-nous assez de risque dans les théories du risque?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(1), pages 111-141, mars.
    2. Machina, Mark J, 2001. "Almost-Objective Uncertainty," University of California at San Diego, Economics Working Paper Series qt3ps1k85f, Department of Economics, UC San Diego.
    3. Machina, Mark J, 2001. "Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-260, November.
    4. Hannsgen, Greg, 2008. "The welfare economics of macroeconomics and chooser-dependent, non-expected utility preferences: A Senian critique with an application to the costs of the business cycle," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(5), pages 1980-1993, October.
    5. Sudhir A. Shah, 2010. "Comparative Risk Aversion When the Outcomes are Vectors," Working Papers id:2907, eSocialSciences.
    6. repec:spo:wpmain:info:hdl:2441/63913pp1o99dr9nneabam7071k is not listed on IDEAS
    7. Arthur Charpentier & Alfred Galichon & Marc Henry, 2012. "Local Utility and Multivariate Risk Aversion," CIRANO Working Papers 2012s-17, CIRANO.
    8. Sudhir A. Shah, 2006. "Comparative risk aversion when the outcomes are vectors," Working papers 149, Centre for Development Economics, Delhi School of Economics.
    9. Robert Jarrow & Siguang Li, 2021. "Concavity, stochastic utility, and risk aversion," Finance and Stochastics, Springer, vol. 25(2), pages 311-330, April.
    10. Mark Machina, 2004. "Almost-objective uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 1-54, July.
    11. repec:hal:spmain:info:hdl:2441/63913pp1o99dr9nneabam7071k is not listed on IDEAS
    12. Horowitz, John K., 2006. "The Becker-DeGroot-Marschak mechanism is not necessarily incentive compatible, even for non-random goods," Economics Letters, Elsevier, vol. 93(1), pages 6-11, October.
    13. Karni, Edi & Schmeidler, David, 1990. "Utility Theory and Uncertainty," Foerder Institute for Economic Research Working Papers 275480, Tel-Aviv University > Foerder Institute for Economic Research.
    14. Alfred Galichon & Arthur Charpentier & Marc Henry, 2012. "Local Utility and Risk Aversion," Post-Print hal-03569250, HAL.
    15. Yonatan Aumann, 2015. "A conceptual foundation for the theory of risk aversion," Discussion Paper Series dp686, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    16. Greg Hannsgen, 2007. "Are the Costs of the Business Cycle 'Trivially Small'?," Economics Working Paper Archive wp_492, Levy Economics Institute.
    17. Arthur Charpentier & Alfred Galichon & Marc Henry, 2016. "Local Utility and Multivariate Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 466-476, May.

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