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BILATERAL RISK SHARING WITH HETEROGENEOUS BELIEFS AND EXPOSURE CONSTRAINTS

Published online by Cambridge University Press:  07 January 2020

Tim J. Boonen Open the ORCID record for Tim J. Boonen [Opens in a new window]  and
Mario Ghossoub Open the ORCID record for Mario Ghossoub [Opens in a new window]
Tim J. Boonen*
Affiliation:
Amsterdam School of Economics University of AmsterdamRoetersstraat 11, 1018 WB, AmsterdamThe Netherlands E-Mail: t.j.boonen@uva.nl
Mario Ghossoub
Affiliation:
Department of Statistics and Actuarial Science University of Waterloo200 University Ave. W., Waterloo N2L 3G1, Canada E-Mail: mario.ghossoub@uwaterloo.ca
*
E-Mail: t.j.boonen@uva.nl
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Abstract

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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 sharingPareto optimalityheterogeneous beliefsprobability distortionexposure constraintsC02D86G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 1 , January 2020 , pp. 293 - 323
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Astin Bulletin 2020

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