The Calculation of Aggregate Loss Distributions from Claim Severity and Claim Count Distributions
by Philip E. Heckman of CNA Insurance Companies, and
Abstract: This paper discusses aggregate loss distributions from the perspective of collective risk theory. An accurate, efficient and practical algorithm is given for calculating cumulative probabilities and excess pure premiums. The input required is the claim severity and claim count distributions. One of the main drawbacks of the collective risk model is the uncertainty of the parameters of the claim severity and claim count distributions. Modifications of the collective risk model are proposed to deal with these problems. These modifications are incorporated into the algorithm. Examples are given illustrating the use of this algorithm. They include (1) calculating the pure premium for a policy with an aggregate limit; (2) calculating the pure premium of an aggregate stop-loss policy for group life insurance; and (3) calculating the insurance charge for a multi-line retrospective rating plan, including a line which is itself subject to an aggregate limit.
Published in: Proceedings of the Casualty Actuarial Society, Vol. 70, No. 133, (May 1983), pp. 22-61.