Robust reinsurance contracts with uncertainty about jump risk

We investigate robust reinsurance contracts in two reinsurance modes, namely proportional reinsurance and excess-loss reinsurance, in a continuous-time principal-agent framework. Insurance claims follow the classic Cramer-Lundberg process. The reinsurer (principal) is concerned about potential ambiguity in the claim intensity, but the insurer (agent) is not. The reinsurer designs a robust reinsurance contract that maximizes the penalty-based multiple-priors utility of terminal wealth, subject to the insurer's incentive compatibility constraint. We derive the analytical expressions of the robust reinsurance contacts. Our results show that the reinsurer dynamically decreases the reinsurance price, which makes the demand for reinsurance increase over time. However, the reinsurer's ambiguity aversion increases the price of reinsurance, which decreases demand. Moreover, the price of excess-loss reinsurance is greater than that of proportional reinsurance. Finally, when the insurer's risk aversion is low or the reinsurer's risk aversion is high, both the insurer and the reinsurer prefer the proportional reinsurance contract.