Recursions for the individual risk model

In the actuarial literature, several exact and approximative recursive methods have been proposed for calculating the distribution of a sum of mutually independent compound Bernoulli distributed random variables. In this paper, we give an overview of these methods. We compare their performance with the straightforward convolution technique by counting the number of dot operations involved in each method. It turns out that in many practicle situations, the recursive methods outperform the convolution method.