Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints

ASTIN Bulletin, 50 (1), 293-323.

29 Pages Posted: 23 Mar 2019 Last revised: 9 Jun 2020

See all articles by Tim J. Boonen

Tim J. Boonen

University of Amsterdam

Mario Ghossoub

University of Waterloo

Date Written: December 11, 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 risk-sharing contract contains allocations that are monotone functions 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

Boonen, Tim J. and Ghossoub, Mario, Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints (December 11, 2019). ASTIN Bulletin, 50 (1), 293-323. , Available at SSRN: or

Tim J. Boonen (Contact Author)

University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB


Mario Ghossoub

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1


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