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Dynamically Consistent α-Maxmin Expected Utility


  • Beißner, Patrick

    (Center for Mathematical Economics, Bielefeld University)

  • Lin, Qian

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)


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

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    References listed on IDEAS

    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. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
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    Dynamic consistency; α-maxmin expected utility; Knightian uncertainty; ambiguity attitude;

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