Optimal allocations with »-maxmin utilities, choquet expected utilities, and prospect theory - Patrick Beißner; Jan Werner (Bielefeld University, Center for Mathematical Economics (IMW), 2022)
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 »-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.
urn:nbn:de:0070-pub-30052863
Keywords: 330; quasidifferential calculus; ambiguity; Pareto optimality; »-MaxMin expected utility; Choquet expected utility; rank-dependent expected utility; Cumulative Prospect Theory