How to (and how not to) compute stop-loss premiums in practice

Abstract

This paper gives guidance for the practical calculation of stop-loss premiums. Some algorithms given in the literature to compute the distribution of the total claims on a life-insurance portfolio are claimed to be exact, but such claims cannot be upheld in practice. On the other hand, it is argued that also for life-insurance the available data is not reliable enough to justify the use of exact algorithms. Though stop-loss premiums provide a better way to compare insurance models than probability functions do, they are harder to handle. The author proposes to look at the variances instead, and proves that they behave rather alike, using some relations between stop-loss premiums and variance. In the absence of really exact methods as well as reliable data, approximate methods like the translated Gamma-approximation become viable, and its use to compute moments of stop-loss benefits is demonstrated. Finally, illustrative numerical examples are given.