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Almost Stochastic Dominance for Most Risk-Averse Decision Makers

Author

Listed:
  • Chunling Luo

    (Singapore-MIT Alliance for Research and Technology, Singapore 138602)

  • Chin Hon Tan

    (Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore 117575)

Abstract

In this paper, we propose a new concept of almost second-degree stochastic dominance (ASSD), which we term almost risk-averse stochastic dominance (ARSD). Compared with existing ASSD conditions, ARSD can exclude extremely risk-averse utility functions. Hence, ARSD is able to reveal clear preferences of most risk-averse decision makers in practice, which are otherwise unable to be revealed. The simple closed-form of ARSD not only makes it easy to use in practice but also provides a clear insight into the preferences of decision makers and the difference in expected values and stochastic dominance violations. Moreover, we show that ARSD can be inferred based on mean and variance alone, and thus it is applicable even when distribution information is incomplete.

Suggested Citation

  • Chunling Luo & Chin Hon Tan, 2020. "Almost Stochastic Dominance for Most Risk-Averse Decision Makers," Decision Analysis, INFORMS, vol. 17(2), pages 169-184, June.
    • Handle: RePEc:inm:ordeca:v:17:y:2020:i:2:p:169-184
    DOI: 10.1287/deca.2019.0402
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    References listed on IDEAS

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    1. Meyer, Jack, 1977. "Choice among distributions," Journal of Economic Theory, Elsevier, vol. 14(2), pages 326-336, April.
    2. Meyer, Jack, 1977. "Second Degree Stochastic Dominance with Respect to a Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 477-487, June.
    3. Bruce A. McCarl & David A. Bessler, 1989. "Estimating An Upper Bound On The Pratt Risk A Version Coefficient When The Utility Function Is Unknown," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 33(1), pages 56-63, April.
    4. Larry Y. Tzeng & Rachel J. Huang & Pai-Ta Shih, 2013. "Revisiting Almost Second-Degree Stochastic Dominance," Management Science, INFORMS, vol. 59(5), pages 1250-1254, May.
    5. Turan G. Bali & Stephen J. Brown & K. Ozgur Demirtas, 2013. "Do Hedge Funds Outperform Stocks and Bonds?," Management Science, INFORMS, vol. 59(8), pages 1887-1903, August.
    6. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
    7. Chun-Hung Chiu & Tsan-Ming Choi, 2016. "Supply chain risk analysis with mean-variance models: a technical review," Annals of Operations Research, Springer, vol. 240(2), pages 489-507, May.
    8. Raskin, Rob & Cochran, Mark J., 1986. "Interpretations And Transformations Of Scale For The Pratt-Arrow Absolute Risk Aversion Coefficient: Implications For Generalized Stochastic Dominance," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 11(2), pages 1-7, December.
    9. Levy, Moshe, 2009. "Almost Stochastic Dominance and stocks for the long run," European Journal of Operational Research, Elsevier, vol. 194(1), pages 250-257, April.
    10. Wu, Jun & Li, Jian & Wang, Shouyang & Cheng, T.C.E., 2009. "Mean-variance analysis of the newsvendor model with stockout cost," Omega, Elsevier, vol. 37(3), pages 724-730, June.
    11. Gary Charness & Edi Karni & Dan Levin, 2007. "Individual and group decision making under risk: An experimental study of Bayesian updating and violations of first-order stochastic dominance," Journal of Risk and Uncertainty, Springer, vol. 35(2), pages 129-148, October.
    12. Robert P. King & Lindon J. Robison, 1981. "An Interval Approach to Measuring Decision Maker Preferences," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 63(3), pages 510-520.
    13. Ishwar Murthy & Sumit Sarkar, 1998. "Stochastic Shortest Path Problems with Piecewise-Linear Concave Utility Functions," Management Science, INFORMS, vol. 44(11-Part-2), pages 125-136, November.
    14. Hanoch, Giora & Levy, Haim, 1970. "Efficient Portfolio Selection with Quadratic and Cubic Utility," The Journal of Business, University of Chicago Press, vol. 43(2), pages 181-189, April.
    15. Levy, Haim, 1994. "Absolute and Relative Risk Aversion: An Experimental Study," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 289-307, May.
    16. Michael Birnbaum, 2005. "A Comparison of Five Models that Predict Violations of First-Order Stochastic Dominance in Risky Decision Making," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 263-287, December.
    17. Ronald A. Howard, 1988. "Decision Analysis: Practice and Promise," Management Science, INFORMS, vol. 34(6), pages 679-695, June.
    18. Love, Ross O. & Robison, Lindon J., 1984. "An Empirical Analysis Of The Intertemporal Stability Of Risk Preference," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 16(1), pages 1-7, July.
    19. Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.
    20. Ilia Tsetlin & Robert L. Winkler & Rachel J. Huang & Larry Y. Tzeng, 2015. "Generalized Almost Stochastic Dominance," Operations Research, INFORMS, vol. 63(2), pages 363-377, April.
    21. Bali, Turan G. & Demirtas, K. Ozgur & Levy, Haim & Wolf, Avner, 2009. "Bonds versus stocks: Investors' age and risk taking," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 817-830, September.
    22. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    23. Peter H. Farquhar, 1984. "State of the Art---Utility Assessment Methods," Management Science, INFORMS, vol. 30(11), pages 1283-1300, November.
    24. Chin Hon Tan & Chunling Luo, 2017. "Clear Preferences Under Partial Distribution Information," Decision Analysis, INFORMS, vol. 14(1), pages 65-73, March.
    25. Matthew J. Sobel, 1994. "Mean-Variance Tradeoffs in an Undiscounted MDP," Operations Research, INFORMS, vol. 42(1), pages 175-183, February.
    26. Haim Levy & Moshe Leshno & Boaz Leibovitch, 2010. "Economically relevant preferences for all observed epsilon," Annals of Operations Research, Springer, vol. 176(1), pages 153-178, April.
    27. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
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