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Dynamically Consistent α-Maxmin Expected Utility

Author

Listed:
  • Beißner, Patrick

    (Center for Mathematical Economics, Bielefeld University)

  • Lin, Qian

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

Abstract

The α-maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of α. In this paper, we derive a recursive, dynamically consistent version of the α-maxmin model. In the continuous-time limit, the resulting dynamic utility function can be represented as a convex mixture between worst and best case, but now at the local, infinitesimal level. We study the properties of the utility function and provide an Arrow- Pratt approximation of the static and dynamic certainty equivalent. We derive a consumption-based capital asset pricing formula and study the implications for derivative valuation under indifference pricing.

Suggested Citation

  • Beißner, Patrick & Lin, Qian & Riedel, Frank, 2018. "Dynamically Consistent α-Maxmin Expected Utility," Center for Mathematical Economics Working Papers 593, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:593
    as

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    File URL: https://pub.uni-bielefeld.de/download/2930436/2930461
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    References listed on IDEAS

    as
    1. Fabio Maccheroni & Massimo Marinacci & Doriana Ruffino, 2013. "Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis," Econometrica, Econometric Society, vol. 81(3), pages 1075-1113, May.
    2. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    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. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
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    More about this item

    Keywords

    Dynamic consistency; α-maxmin expected utility; Knightian uncertainty; ambiguity attitude;
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