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Stochastic Dominance Tests for Decreasing Absolute Risk Aversion. I. Discrete Random Variables

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  • R. G. Vickson

    (University of Waterloo)

Abstract

Stochastic dominance (SD) theory is concerned with orderings of random variables by classes of utility functions characterized solely in terms of general properties. This paper discusses a type of stochastic dominance, called DSD, which is denned by the utility functions having decreasing absolute risk-aversion. Necessary and sufficient conditions for DSD are presented for discrete random variables which, after the possible addition of points of zero probability, are concentrated on finitely many equally-spaced points. The problem is cast as a nonlinear program, which is solved through an efficient dynamic programming routine. Examples are presented to illustrate the increased effectiveness of DSD relative to previous types of stochastic dominance.

Suggested Citation

  • R. G. Vickson, 1975. "Stochastic Dominance Tests for Decreasing Absolute Risk Aversion. I. Discrete Random Variables," Management Science, INFORMS, vol. 21(12), pages 1438-1446, August.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:12:p:1438-1446
    DOI: 10.1287/mnsc.21.12.1438
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    Cited by:

    1. Zentner, Robert P. & Greene, Duty D. & Hickenbotham, Terry L. & Eidman, Vernon R., 1981. "Ordinary And Generalized Stochastic Dominance: A Primer," Staff Papers 14184, University of Minnesota, Department of Applied Economics.
    2. Andrey Lizyayev, 2012. "Stochastic dominance efficiency analysis of diversified portfolios: classification, comparison and refinements," Annals of Operations Research, Springer, vol. 196(1), pages 391-410, July.
    3. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.
    4. Thierry Post & Valerio Potì, 2017. "Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood," Management Science, INFORMS, vol. 63(1), pages 153-165, January.
    5. Pirtea Marilen & Boţoc Claudiu, 2008. "Risk Aversion Behavior. Relationships Between Risk Aversion, Prudence And Cautiousness," Annales Universitatis Apulensis Series Oeconomica, Faculty of Sciences, "1 Decembrie 1918" University, Alba Iulia, vol. 1(10), pages 1-32.
    6. Thierry Post & Milos Kopa, 2015. "Portfolio Choice based on Third-degree Stochastic Dominance, With an Application to Industry Momentum," Koç University-TUSIAD Economic Research Forum Working Papers 1527, Koc University-TUSIAD Economic Research Forum.
    7. Christian Gollier & Miles S. Kimball, 2018. "New methods in the classical economics of uncertainty: comparing risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 5-23, May.
    8. Basso, Antonella & Funari, Stefania, 2001. "A data envelopment analysis approach to measure the mutual fund performance," European Journal of Operational Research, Elsevier, vol. 135(3), pages 477-492, December.
    9. Thierry Post & Yi Fang & Miloš Kopa, 2015. "Linear Tests for Decreasing Absolute Risk Aversion Stochastic Dominance," Management Science, INFORMS, vol. 61(7), pages 1615-1629, July.
    10. Zheng, Buhong, 2000. "Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings," Journal of Economic Theory, Elsevier, vol. 95(1), pages 116-137, November.
    11. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    12. Thorlund-Petersen, Lars, 2001. "Third-degree stochastic dominance and axioms for a convex marginal utility function," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 167-199, March.
    13. Courtois, Olivier Le & Xu, Xia, 2023. "Semivariance below the maximum: Assessing the performance of economic and financial prospects," Journal of Economic Behavior & Organization, Elsevier, vol. 209(C), pages 185-199.
    14. Thierry Post & Miloš Kopa, 2017. "Portfolio Choice Based on Third-Degree Stochastic Dominance," Management Science, INFORMS, vol. 63(10), pages 3381-3392, October.
    15. Antonella Basso & Paolo Pianca, 1997. "On the relative efficiency of nth order and DARA stochastic dominance rules," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 207-222.
    16. Andrey Lizyayev, 2010. "Stochastic Dominance Efficiency Analysis of Diversified Portfolios: Classification, Comparison and Refinements," Tinbergen Institute Discussion Papers 10-084/2, Tinbergen Institute.

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