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Optimal Allocations with $\alpha$-MaxMin Utilities, Choquet Expected Utilities, and Prospect Theory

Author

Listed:
  • Beißner, Patrick

    (Center for Mathematical Economics, Bielefeld University)

  • Werner, Jan

    (Center for Mathematical Economics, Bielefeld University)

Abstract

The analysis of optimal risk sharing has been thus far largely restricted to non-expected utility models with concave utility functions, where concavity is an expression of ambiguity aversion and/or risk aversion. This paper extends the analysis to $\alpha$-maxmin expected utility, Choquet expected utility, and Cumulative Prospect Theory, which accommodate ambiguity seeking and risk seeking attitudes. We introduce a novel methodology of quasidifferential calculus of Demyanov and Rubinov (1986, 1992) and argue that it is particularly well-suited for the analysis of these three classes of utility functions which are neither concave nor differentiable. We provide characterizations of quasidifferentials of these utility functions, derive first-order conditions for Pareto optimal allocations under uncertainty, and analyze implications of these conditions for risk sharing with and without aggregate risk.

Suggested Citation

  • Beißner, Patrick & Werner, Jan, 2025. "Optimal Allocations with $\alpha$-MaxMin Utilities, Choquet Expected Utilities, and Prospect Theory," Center for Mathematical Economics Working Papers 722, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:722
    as

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    File URL: https://pub.uni-bielefeld.de/download/3005286/3005287
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    References listed on IDEAS

    as
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