Séminaire de mathématiques actuarielles et financières: «Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints»
Conférencier: Mario Ghossoub, University of Waterloo
Résumé/abstract: We study bilateral risk sharing under no aggregate uncertainty, where one agent has Expected-Utility (EU) 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 of one agent, 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 contract is a monotone function of the likelihood ratio, where the latter is obtained from Lebesgue’s Decomposition Theorem. Moreover, unlike in the case where both agents have EU preferences, common beliefs might still lead to a risk-sharing situation in which betting is Pareto-improving; and betting might not always be Pareto-improving when beliefs are divergent. We also show that if agents disagree about likelihoods but not about zero-probability events, then Pareto-optimal allocations are deterministic (no-betting allocations), as long as the counterparty’s level of probabilistic risk-aversion exceeds the level of belief heterogeneity between the agents.
(This is joint work with Tim Boonen)
Date / heure