Risk sharing with expected and dual utilities

Abstract

This paper analyzes optimal risk sharing among agents that are endowed with either expected utility preferences or with dual utility preferences. We find that Pareto optimal risk redistributions and the competitive equilibria can be obtained via bargaining with a hypothetical representative agent of expected utility maximizers and a hypothetical representative agent of dual utility maximizers. The representative agent of expected utility maximizers resembles an average risk-averse agent, whereas representative agent of dual utility maximizers resembles an agent that has lowest aversion to mean-preserving spreads. This bargaining leads to an allocation of the aggregate risk to both groups of agents. The optimal contract for the expected utility maximizers is proportional to their allocated risk, and the optimal contract for the dual utility maximizing agents is given by tranching of their allocated risk. We show a method to derive equilibrium prices. We identify a condition under which prices are locally independent of the expected utility functions, and given in closed form. Moreover, we characterize uniqueness of the competitive equilibrium.