Stochastic Excess-of-Loss Pricing within a Financial Framework

This paper is aimed at the practicing actuary to introduce the theory of extreme values and a financial framework to price excess-of-loss reinsurance treaties. We introduce the reader to extreme value theory via the classical central limit theorem. Two key results in extreme value theory are presented and illustrated with concrete examples. The discussion then moves on to collective risk models, considerations in modeling tail events, and measures of risk. All these concepts are brought together with the modeling of actual losses. In the last section of the paper all previous elements are brought together with a financial framework for the pricing of a layer of reinsurance. The cash flows between the insurance company and its equity holders are modeled.