On a simple quasi-Monte Carlo approach for classical ultimate ruin probabilities

This note discusses a simple quasi-Monte Carlo method to evaluate numerically the ultimate ruin probability in the classical compound Poisson risk model. The key point is the Pollaczek–Khintchine representation of the non-ruin probability as a series of convolutions. Our suggestion is to truncate the series at some appropriate level and to evaluate the remaining convolution integrals by quasi-Monte Carlo techniques. For illustration, this approximation procedure is applied when claim sizes have an exponential or generalized Pareto distribution.