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Modifying the Mean-Variance Approach to Avoid Violations of Stochastic Dominance

  • Pavlo R. Blavatskyy

    ()

    (Institute of Public Finance, University of Innsbruck, A-6020 Innsbruck, Austria)

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    The mean-variance approach is an influential theory of decision under risk proposed by Markowitz (Markowitz, H. 1952. Portfolio selection. J. Finance 7(1) 77-91). The mean-variance approach implies violations of first-order stochastic dominance not commonly observed in the data. This paper proposes a new model in the spirit of the classical mean-variance approach without violations of stochastic dominance. The proposed model represents preferences by a functional U(L) - \rho \cdot r(L), where U(L) denotes the expected utility of lottery L, \rho \in [-1, 1] is a subjective constant, and r(L) is the mean absolute (utility) semideviation of lottery L. The model comprises a linear trade-off between expected utility and utility dispersion. The model can accommodate several behavioral regularities such as the Allais paradox and switching behavior in Samuelson's example.

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    File URL: http://dx.doi.org/10.1287/mnsc.1100.1224
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 56 (2010)
    Issue (Month): 11 (November)
    Pages: 2050-2057

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    Handle: RePEc:inm:ormnsc:v:56:y:2010:i:11:p:2050-2057
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    1. Bernasconi, Michele, 1994. "Nonlinear Preferences and Two-Stage Lotteries: Theories and Evidence," Economic Journal, Royal Economic Society, vol. 104(422), pages 54-70, January.
    2. John Hey, . "Does Repetition Improve Consistency?," Discussion Papers 99/28, Department of Economics, University of York.
    3. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    4. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-96, March.
    5. K. Borch, 1969. "A Note on Uncertainty and Indifference Curves," Review of Economic Studies, Oxford University Press, vol. 36(1), pages 1-4.
    6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
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