How much is optimal reinsurance degraded by error?

Abstract

The literature on optimal reinsurance does not deal with how much the effectiveness of such solutions is degraded by errors in parameters and models. The issue is investigated through both asymptotics and numerical studies. It is shown that the rate of degradation is often $O(1/n)$ as the sample size $n$ of historical observations becomes infinite. Criteria based on Value at Risk are exceptions that may achieve only $O(1/\sqrt{n})$. These theoretical results are supported by numerical studies. A Bayesian perspective on how to integrate risk caused by parameter error is offered as well.