How much is optimal reinsurance degraded by error?

TL;DR

This paper investigates how errors in parameters and models reduce the effectiveness of optimal reinsurance solutions, revealing degradation rates and proposing Bayesian integration methods.

Contribution

It provides asymptotic and numerical analysis of reinsurance degradation due to parameter errors and introduces a Bayesian approach to mitigate this risk.

Findings

Degradation rate often O(1/n) with increasing data

Value at Risk criteria may degrade at O(1/√n)

Numerical studies support theoretical results

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.