Optimal allocations with α-MaxMin utilities, Choquet expected utilities, and Prospect Theory - Patrick Beißner; Jan Werner (Theoretical Economics, 2023)
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: C61; D50; D60; D81; 330; ambiguity; Choquet expected utility; cumulative prospect theory; Pareto optimality; Quasidifferential calculus; rank-dependent expected utility; »-MaxMin expected utility