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A Smooth Model of Decision,Making Under Ambiguity

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  • Sujoy Mukerji
  • Peter Klibanoff

Abstract

We propose and axiomatize a model of preferences over acts such that the decision maker evaluates acts according to the expectation (over a set of probability measures) of an increasing transformation of an act`s expected utility. This expectation is calculated using a subjective probability over the set of probability measures that the decision maker thinks are relevant given her subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker`s subjective information, and ambiguity attitude, a characteristic of the decision maker`s tastes. We show that attitudes towards risk are characterized by the shape of the von Neumann-Morgenstern utility function, as usual, while attitudes towards ambiguity are characterized by the shape of the increasing transformation applied to expected utilities. We show that the negative exponential form of this transformation is the special case of constant ambiguity aversion. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures. This characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by Epstein-Zhang (2001) and Ghirardato-Marinacci (2002). One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g. Ellsberg`s Paradox, etc.). The Maxmin EU model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion. Two illustrative applications to portfolio choice are offered.

Suggested Citation

  • Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:113
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    References listed on IDEAS

    as
    1. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    2. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    3. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    4. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    5. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
    6. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
    9. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    10. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-1272, November.
    11. Loomes, Graham & Segal, Uzi, 1994. "Observing Different Orders of Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 9(3), pages 239-256, December.
    12. Simon Grant & Atsushi Kajii & Ben Polak, 2000. "Temporal Resolution of Uncertainty and Recursive Non-Expected Utility Models," Econometrica, Econometric Society, vol. 68(2), pages 425-434, March.
    13. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    14. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    15. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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    More about this item

    Keywords

    ambiguity; uncertainty; ambiguity aversion; uncertainty aversion; Ellsberg Paradox;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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