A RUIN FUNCTION APPROXIMATION

Abstract

This paper derives a formula for approximating the ruin function of collective risk theory. This formula is simple to calculate and is based on the distribution of claims and the security loading. It is partially based on several papers in the Transactions dealing with approximating the distribution of total claims in collective risk theory. The derivations for the formula are given in the Appendix. Use of the ruin function in setting retention limits is explained. The following questions are answered, for example. If the retention level is set at $X, what fund is needed in order that the adverse fluctuation will stay below its value with high probability, say, 0.99? Various retention levels and funds are compared for practical distributions. If the upper limit on adverse fluctuation is $Y, what is the corresponding retention level? Use of the ruin function in deciding the amount of initial capital for a new line of business is discussed.