Recursive Procedure for Calculation of Some Compound Distributions

We consider compound distributions where the counting distribution has the property that the ratio between successive probabilities may be written as the ratio of two polynomials. We derive a recursive algorithm for the compound distribution, which is more efficient than the one suggested by PANJER & WILLMOT (1982) and WILLMOT & PANJER (1987). We also derive a recursive an application of the recursion to the problem of calculating the probability of ruin in a particular mixed Poisson process.