Lattice Rules for the Simulation of Ruin Problems

Lattice rules are a quasi-Monte Carlo method, an alternative to the Monte Carlo method for multidimensional numerical integration. The measures of performance that we estimate by simulation can be seen as the values of integrals in large dimensions. Therefore, instead of the usual Monte Carlo method, one can use lattice rules in simulation. In this paper, we compare these rules to the Monte Carlo method to simulate the surplus process of an insurance company, in order to estimate the ruin probability. We give results using diierent simulation techniques and also try diierent parameters, in order to see how this aaects the relative performance of these two methods.