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

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  • Pavlo R. Blavatskyy

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

Abstract

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.

Suggested Citation

  • Pavlo R. Blavatskyy, 2010. "Modifying the Mean-Variance Approach to Avoid Violations of Stochastic Dominance," Management Science, INFORMS, vol. 56(11), pages 2050-2057, November.
    • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:11:p:2050-2057
    DOI: 10.1287/mnsc.1100.1224
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    References listed on IDEAS

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    Cited by:

    1. Joaquín Gómez Miñambres & Mark Schneider, 2019. "Carrots and Sticks: Optimal Contracting with Skewness Preference and Ambiguity Aversion," Working Papers 19-02, Chapman University, Economic Science Institute.
    2. Pavlo Blavatskyy, 2021. "A simple non-parametric method for eliciting prospect theory's value function and measuring loss aversion under risk and ambiguity," Theory and Decision, Springer, vol. 91(3), pages 403-416, October.
    3. Behnam Malakooti & Mohamed Komaki & Camelia Al-Najjar, 2021. "Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad," Decision Analysis, INFORMS, vol. 18(1), pages 41-77, March.
    4. Enrica Carbone & Xueqi Dong & John Hey, 2017. "Elicitation of preferences under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 54(2), pages 87-102, April.
    5. Bettina Klose & Paul Schweinzer, 2022. "Auctioning risk: the all-pay auction under mean-variance preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 881-916, June.
    6. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    7. Schoch, Daniel, 2017. "Generalised mean-risk preferences," Journal of Economic Theory, Elsevier, vol. 168(C), pages 12-26.
    8. Blavatskyy, Pavlo, 2013. "Which decision theory?," Economics Letters, Elsevier, vol. 120(1), pages 40-44.
    9. Latifa Ghalayini & Dana Deeb, 2021. "Utility Measurement in Integrative Negotiation," Information Management and Business Review, AMH International, vol. 13(1), pages 1-15.
    10. Mark Schneider, 2019. "A Bias Aggregation Theorem," Working Papers 19-03, Chapman University, Economic Science Institute.
    11. Pavlo Blavatskyy, 2023. "Expected return—expected loss approach to optimal portfolio investment," Theory and Decision, Springer, vol. 94(1), pages 63-81, January.
    12. Post, Thierry & Kopa, Miloš, 2013. "General linear formulations of stochastic dominance criteria," European Journal of Operational Research, Elsevier, vol. 230(2), pages 321-332.
    13. Pavlo Blavatskyy, 2018. "A second-generation disappointment aversion theory of decision making under risk," Theory and Decision, Springer, vol. 84(1), pages 29-60, January.
    14. Blavatskyy, Pavlo R., 2012. "The Troika paradox," Economics Letters, Elsevier, vol. 115(2), pages 236-239.

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