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Stochastic Dominance Tests for Decreasing Absolute Risk-Aversion II: General Random Variables

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  • R. G. Vickson

    (University of Waterloo)

Abstract

Necessary and sufficient conditions are given for stochastic dominance over the class of decreasing absolute risk-averse utility functions. The random variables being compared may be continuous as well as discrete but are assumed to be bounded from below, to have finite means, to have only finitely many mass points in finite intervals, and to have cumulative distribution functions which cross one another only finitely many times, or touch one another only finitely many times in finite intervals. The precise forms of the dominance tests depend upon the number of times the distribution functions cross. An example of the DSD test is presented, and a dynamic programming algorithm for carrying out the general test is given.

Suggested Citation

  • R. G. Vickson, 1977. "Stochastic Dominance Tests for Decreasing Absolute Risk-Aversion II: General Random Variables," Management Science, INFORMS, vol. 23(5), pages 478-489, January.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:5:p:478-489
    DOI: 10.1287/mnsc.23.5.478
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. McCamley, Francis & Kliebenstein, James B., 1986. "Necessary Conditions For Dsd Efficiency Of Mixtures Of Risky Alternatives," 1986 Annual Meeting, July 27-30, Reno, Nevada 278149, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Cochran, Mark J., 1986. "Stochastic Dominance: The State Of The Art In Agricultural Economics," Regional Research Projects > 1986: S-180 Annual Meeting, March 23-26, 1986, Tampa, Florida 271995, Regional Research Projects > S-180: An Economic Analysis of Risk Management Strategies for Agricultural Production Firms.
    6. 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.
    7. Zheng, Buhong, 2000. "Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings," Journal of Economic Theory, Elsevier, vol. 95(1), pages 116-137, November.
    8. Light, Bar & Perlroth, Andres, 2021. "The Family of Alpha,[a,b] Stochastic Orders: Risk vs. Expected Value," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    9. Thierry Post & Miloš Kopa, 2017. "Portfolio Choice Based on Third-Degree Stochastic Dominance," Management Science, INFORMS, vol. 63(10), pages 3381-3392, October.
    10. W. Wong & R. Chan, 2008. "Prospect and Markowitz stochastic dominance," Annals of Finance, Springer, vol. 4(1), pages 105-129, January.
    11. 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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