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Repeated Gambles, Learning, and Risk Aversion

Author

Listed:
  • Kevin F. McCardle

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27706)

  • Robert L. Winkler

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27706)

Abstract

We analyze a decision problem with repeated gambles and find that under some seemingly reasonable risk-averse utility functions, recommended behavior for the initial decision can be highly risk-taking and counterintuitive. Further analysis reveals that the derived utility function for the return on the first gamble is discontinuous because gains or losses carry with them positive or negative signals regarding future prospects. A variant of the basic model without a discontinuity in derived utility has essentially the same implications. The issues raised in this paper present no conceptual difficulties for the standard expected utility theory; in principle, we can model the grand world and understand fully all implications of grand-world utility functions. In practice, however, this ideal may not always be attainable and as a result we may be faced with serious modeling and assessment problems.

Suggested Citation

  • Kevin F. McCardle & Robert L. Winkler, 1992. "Repeated Gambles, Learning, and Risk Aversion," Management Science, INFORMS, vol. 38(6), pages 807-818, June.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:6:p:807-818
    DOI: 10.1287/mnsc.38.6.807
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    Citations

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    Cited by:

    1. Manel Baucells & Rakesh K. Sarin, 2019. "The Myopic Property in Decision Models," Decision Analysis, INFORMS, vol. 16(2), pages 128-141, June.
    2. Rose D. Baker & Ian G. McHale, 2013. "Optimal Betting Under Parameter Uncertainty: Improving the Kelly Criterion," Decision Analysis, INFORMS, vol. 10(3), pages 189-199, September.
    3. Gollier Christian, 2004. "Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-35, September.
    4. Gordon Hazen & Emanuele Borgonovo & Xuefei Lu, 2023. "Information Density in Decision Analysis," Decision Analysis, INFORMS, vol. 20(2), pages 89-108, June.
    5. Alfred Müller & Marco Scarsini & Ilia Tsetlin & Robert L. Winkler, 2017. "Between First- and Second-Order Stochastic Dominance," Management Science, INFORMS, vol. 63(9), pages 2933-2947, September.
    6. Anil Gaba & Ilia Tsetlin & Robert L. Winkler, 2004. "Modifying Variability and Correlations in Winner-Take-All Contests," Operations Research, INFORMS, vol. 52(3), pages 384-395, June.
    7. Douglas W. Blackburn & Andrey D. Ukhov, 2013. "Individual vs. Aggregate Preferences: The Case of a Small Fish in a Big Pond," Management Science, INFORMS, vol. 59(2), pages 470-484, August.
    8. Gollier, Christian, 1994. "Second-Best Risk Sharing With Incomplete Contracts," Working Papers 015, Risk and Insurance Archive.
    9. Saaty, Thomas L., 2006. "Rank from comparisons and from ratings in the analytic hierarchy/network processes," European Journal of Operational Research, Elsevier, vol. 168(2), pages 557-570, January.
    10. Gollier, Christian, 2002. "Optimal Prevention of Unknown Risks: A Dynamic Approach with Learning," IDEI Working Papers 139, Institut d'Économie Industrielle (IDEI), Toulouse.

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