Frequency Formulas for Determining Stop-Loss Reinsurance Premiums

Abstract

The calculation of a premium for stop-loss reinsurance calls for the use of a frequency distribution for measuring variation in the total sum to be paid out for claims in one year. This distribution (often assumed to be a continuous function) is usually expressed as the combination of functions for two variables. These two variables are the number of claims and the amount of one claim. Reasonable mathematical expressions are available for the number of claims but not for distributions of claim amounts for the usual classifications by line of insurance. The combination of the two functions presents practically an insolvable expression. In order to proceed satisfactorily, the insurance exposure and resulting claims must be separated into sub-classifications that will have a central mean value and relatively small deviations from the mean. If the deviations from the mean for each sub-class are sufficiently small, the distribution of the number of claims expressed as a continuous function can be used to measure the variations in total sum paid out. If the deviations are not small enough for this procedure but the distribution of claim amounts retains one central mean value, a special development representing the combination of a Poisson distribution for the number of claims and of a Gamma function for the amount of one claim is provided.