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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*
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
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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.

Type
Research Article
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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