BILATERAL RISK SHARING WITH HETEROGENEOUS BELIEFS AND EXPOSURE CONSTRAINTS

Tim J. Boonen and Mario Ghossoub

ASTIN Bulletin, 2020, vol. 50, issue 1, 293-323

Abstract: 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 risk-sharing contract contains allocations that are monotone functions of the likelihood ratio, where the latter is obtained from Lebesgue’s Decomposition Theorem.

Date: 2020
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