Pareto Optimality and Robust Optimisation

The optimal reinsurance contract has been a topic of great interest for many decades in the insurance literature. The primary insurer aims to share the risk with one or many other reinsurers for a premium. Finding the optimal contract has been a topic for a long time in insurance economics literature. Depending on how the problem is put, the solutions are different, but layer reinsurance appears to be optimal contract, which confirms the existing empirical evidence. In this talk, we will focus on finding the optimal contract from the perspective of primary reinsurer or from the perspective of all insurers. Interestingly, all solutions are optimal Pareto when all risk preferences have the translation invariance property. The robustness of the reinsurance contract is also discussed. Finally, we will show that introducing of some constraints, the optimal contract is no longer a layer reinsurance and instead, a proportional reinsurance contract appears to be the optimal one.