Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints
30 Pages Posted: 23 Mar 2019
Date Written: March 1, 2019
This paper studies bilateral risk sharing under no aggregate uncertainty, where one agent has Expected-Utility preferences and the other agent has Rank-Dependent Utility preferences with a general probability distortion function. We impose exogenous constraints on the risk exposure for both agents, and we allow for any type or level of belief heterogeneity. We show that Pareto-optimal risk-sharing contracts can be obtained via a constrained utility maximization under a participation constraint of the other agent. This allows us to give an explicit characterization of optimal risk-sharing contracts. In particular, we show that an optimal contract is a monotone function of the likelihood ratio, where the latter is obtained from Lebesgue's Decomposition Theorem.
Keywords: Risk Sharing, Pareto Optimality, Heterogeneous Beliefs, Probability Distortion, Exposure Constraints
JEL Classification: C02, D86, G22
Suggested Citation: Suggested Citation