Theoretical Economics 18 (2023), 993–1022

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### Optimal allocations with α-MaxMin utilities, Choquet expected utilities, and Prospect Theory

*Patrick Beissner, Jan Werner*

#### 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 α-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.

Keywords: Ambiguity, risk sharing, non-convex preferences, Pareto optimality, quasidifferential, Clarke subdifferential, α-MaxMin expected utility, Choquet expected utility, rank-dependent expected utility, Cumulative Prospect Theory

JEL classification: C61, D50, D60, D81

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