We are Living on the Edge: Managing Extreme-Severity Claims Using Extreme Value Theory

Abstract

Claims with high severity and low probability constitute a high risk for the insurance market. One tool to deal with this kind of event is the Extreme Value Theory (EVT). The main goal of this article is to apply the EVT to Actuarial Science using a different estimator for parameters, allowing the calculation of pure reinsurance premiums and the choice for the retention limit for insurance companies. The execution was split into two parts: (i) comparing the estimators through simulations, and; (ii) using data from 5 SUSEP lines of business with different natures, intending to estimate some extreme value statistics. In simulation studies, the Pickands estimator was very promising, but the limited amount of data resulted in a great variance when applied to real cases. Lastly, we concluded that the EVT is a powerful tool for insurance, capturing the behavior of extreme clams amount better than traditional models.

Keywords:
Insurance; Extreme values; Expected shortfall; High quantiles estimation