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Allais, Ellsberg, and preferences for hedging

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  • Dean, Mark

    (Department of Economics, Columbia University)

  • Ortoleva, Pietro

    (Department of Economics, Columbia University)

Abstract

Two of the most well-known regularities observed in preferences under risk and uncertainty are ambiguity aversion and the Allais paradox. We study the behavior of an agent who can display both tendencies simultaneously. We introduce a novel notion of preference for hedging that applies to both objective lotteries and uncertain acts. We show that this axiom, together with other standard ones, is equivalent to a representation in which the agent 1) evaluates ambiguity using multiple priors, as in the model of Gilboa and Schmeidler [1989] and 2) evaluates objective lotteries by distorting probabilities, as in the Rank Dependent Utility model, but using the worst from a set of distortions. We show that a preference for hedging is not sufficient to guarantee Ellsberg-like behavior if the agent violates Expected Utility for objective lotteries; we provide a novel axiom that characterizes this case, linking the distortions for objective and subjective bets

Suggested Citation

  • Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
  • Handle: RePEc:the:publsh:1960
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    References listed on IDEAS

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    Cited by:

    1. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    2. Jean Baccelli, 2018. "Risk attitudes in axiomatic decision theory: a conceptual perspective," Theory and Decision, Springer, vol. 84(1), pages 61-82, January.
    3. Aurélien Baillon & Olivier L’Haridon, 2021. "Discrete Arrow–Pratt indexes for risk and uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1375-1393, November.
    4. David Dillenberger & Andrew Postlewaite & Kareen Rozen, 2011. "Optimism and Pessimism with Expected Utility, Third Version," PIER Working Paper Archive 13-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 26 Dec 2012.
    5. Wakker, Peter P. & Yang, Jingni, 2019. "A powerful tool for analyzing concave/convex utility and weighting functions," Journal of Economic Theory, Elsevier, vol. 181(C), pages 143-159.
    6. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    7. David Dillenberger & Andrew Postlewaite & Kareen Rozen, 2013. "Optimism and Pessimism with Expected Utility, Fifth Version," PIER Working Paper Archive 15-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 23 Feb 2015.
    8. Bommier, Antoine, 2017. "A dual approach to ambiguity aversion," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 104-118.
    9. Matthew Kovach, 2021. "Ambiguity and Partial Bayesian Updating," Papers 2102.11429, arXiv.org, revised Jan 2022.
    10. MacLeod, W Bentley, 2016. "Human capital: Linking behavior to rational choice via dual process theory," Labour Economics, Elsevier, vol. 41(C), pages 20-31.
    11. DeJarnette, Patrick & Dillenberger, David & Gottlieb, Daniel & Ortoleva, Pietro, 2020. "Time lotteries and stochastic impatience," LSE Research Online Documents on Economics 102564, London School of Economics and Political Science, LSE Library.
    12. Larry G. Epstein & Yoram Halevy, 2019. "Hard-to-Interpret Signals," Working Papers tecipa-634, University of Toronto, Department of Economics.
    13. Patrick DeJarnette & David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2014. "Time Lotteries, Second Version," PIER Working Paper Archive 15-026v2, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 12 Jan 2018.
    14. Patrick DeJarnette & David Dillenberger & Daniel Gottlieb & Pietro Ortoleva, 2020. "Time Lotteries and Stochastic Impatience," Econometrica, Econometric Society, vol. 88(2), pages 619-656, March.
    15. David Dillenberger & Andrew Postlewaite & Kareen Rozen, 2011. "Optimism and Pessimism with Expected Utility, Fourth Version," PIER Working Paper Archive 13-068, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Nov 2013.
    16. Jean Baccelli, 2018. "Risk Attitudes in Axiomatic Decision Theory: a Conceptual Perspective," Post-Print hal-01620886, HAL.
    17. Stefan Trautmann & Peter P. Wakker, 2018. "Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 83-116, February.
    18. Ghirardato, Paolo & Pennesi, Daniele, 2020. "A general theory of subjective mixtures," Journal of Economic Theory, Elsevier, vol. 188(C).
    19. Abdellaoui, Mohammed & Wakker, Peter P., 2020. "Savage for dummies and experts," Journal of Economic Theory, Elsevier, vol. 186(C).

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    More about this item

    Keywords

    Ambiguity aversion; Allais paradox; Ellsberg paradox; hedging; multiple priors; subjective mixture; probability weighting; rank dependent utility;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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