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Revisiting Almost Second-Degree Stochastic Dominance

Author

Listed:
  • Larry Y. Tzeng

    (Department of Finance, National Taiwan University, Taipei 106, Taiwan; and Risk and Insurance Research Center, National Chengchi University, Taipei 116, Taiwan)

  • Rachel J. Huang

    (Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei 106, Taiwan; and Risk and Insurance Research Center, National Chengchi University, Taipei 116, Taiwan)

  • Pai-Ta Shih

    (Department of Finance, National Taiwan University, Taipei 106, Taiwan)

Abstract

Leshno and Levy [Leshno M, Levy H (2002) Preferred by “all” and preferred by “most” decision makers: Almost stochastic dominance. Management Sci. 48(8):1074--1085] established almost stochastic dominance to reveal preferences for most rather than all decision makers with an increasing and concave utility function. In this paper, we first provide a counterexample to the main theorem of Leshno and Levy related to almost second-degree stochastic dominance. We then redefine this dominance condition and show that the newly defined almost second-degree stochastic dominance is the necessary and sufficient condition to rank distributions for all decision makers excluding the pathological concave preferences. We further extend our results to almost higher-degree stochastic dominance. This paper was accepted by Peter Wakker, decision analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:59:y:2013:i:5:p:1250-1254
    DOI: 10.1287/mnsc.1120.1616
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    References listed on IDEAS

    as
    1. Denuit, M. & Eeckhoudt L., 2010. "A general index of absolute risk attitude," LIDAM Discussion Papers ISBA 2010013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    3. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    4. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    5. Michel M. Denuit & Louis Eeckhoudt, 2010. "A General Index of Absolute Risk Attitude," Management Science, INFORMS, vol. 56(4), pages 712-715, April.
    6. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    8. 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.
    9. 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.
    10. Denuit, M. & Eeckhoudt, L., 2010. "A General Index of Absolute Risk Attitude," LIDAM Reprints ISBA 2010026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. 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.
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