Recursive Evaluation of a Family of Compound Distributions
by Harry H. Panjer of the University of Waterloo
Introduction: Compound distributions such as the compound Poisson and the compound negative binomial are used extensively in the theory of risk to model the distribution of the total claims incurred in a fixed period of time. The usual method of evaluating the distribution function requires the computation of many convolutions of the conditional distribution of the amount of a claim given that a claim has occurred. When the expected number of claims is large, the computation can become unwieldy even with modern large scale electronic computers.
Published in: Astin Bulletin, Vol. 12, No. 1, (July 1981), pp. 22-26.