Optimal allocations with α-maxmin utilities, Choquet expected utilities, and prospect theory

The analysis of optimal risk sharing has been thus far largely restricted to nonexpected 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.