Recursions for the individual model

Recently, Waldmann considered an algorithm to compute the aggregate claims distribution in the individual life model which is an efficient reformulation of the original exact algorithm of De Pril. In this paper we will show that in practice the approximations as proposed by De Pril are still more efficient than the exact algorithm of Waldmann both in terms of the number of computations required and of the memory occupied by intermediate results. Furthermore we will generalize the algorithm of Waldmann to arbitrary claim amount distributions. We will compare this algorithm with respect to efficiency with the algorithms that were derived by De Pril for this model. It turns out that the approximations of De Pril are most efficient for practical computations.