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.
Highlights
Bilateral risk sharing is a risk transfer and reallocation mechanism popularized by the prevalence of over-the-counter trading, that is, direct trading between two parties without the supervision of an exchange
We characterize optimal risk-sharing contracts for any type or level of belief heterogeneity and any probability distortion function, and we provide an explicit description of the optimal risk-sharing contract for the decision maker (DM) subject to a participation constraint of the counterparty
The counterparty is endowed with rank-dependent utility (RDU) preferences (Quiggin, 1982, 1991, 1993), which admit a representation in terms of a Choquet integral
Summary
Bilateral risk sharing is a risk transfer and reallocation mechanism popularized by the prevalence of over-the-counter trading, that is, direct trading between two parties without the supervision of an exchange. As an exception, Boonen (2017) studies Pareto-optimal risk sharing with both expected and dual utilities All of these approaches impose assumptions that ensure that the optimal contracts are comonotonic.. We characterize optimal risk-sharing contracts for any type or level of belief heterogeneity and any probability distortion function, and we provide an explicit description of the optimal risk-sharing contract for the DM subject to a participation constraint of the counterparty. It has a simple two-part structure: the DM receives a maximal wealth transfer on an event to which the counterparty assigns zero probability, and an explicit solution on the complement of this event.
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