On the efficient evaluation of ruin probabilities for completely monotone claim distributions

In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed by Trefethen et al. [12]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical justification for the method. We also show that under weaker assumptions on the claim size distribution, the method may still perform reasonably well in some cases. This in particular provides an efficient alternative to a related method proposed by Thorin [10]. A number of numerical illustrations for the performance of this procedure is provided for both completely monotone and other types of random variables.