Model Ambiguity in Risk Sharing with Monotone Mean-Variance

Abstract: We consider the problem of an agent who faces losses over a finite time horizon and may choose to share some of these losses with a counterparty. The agent is uncertain about the true loss distribution and has multiple models for the losses. Their goal is to optimize a mean-variance type criterion with model ambiguity through risk sharing. We construct such a criterion by adapting the monotone mean-variance preferences of Maccheroni et al. (2009) to the multiple models setting and exploit a dual representation to mitigate time-consistency issues. Assuming a Cram\'er-Lundberg loss model, we fully characterize the optimal risk sharing contract and the agent's wealth process under the optimal strategy. Furthermore, we prove that the strategy we obtain is admissible and prove that the value function satisfies the appropriate verification conditions. Finally, we apply the optimal strategy to an insurance setting using data from a Spanish automobile insurance portfolio, where we obtain differing models using cross-validation and provide numerical illustrations of the results.