Rare-event simulation for multidimensional random walks with t distributed increments

In this paper we consider a stylized multidimensional rare-event simulation problem for a heavy-tailed process. More precisely, the problem of e¢ cient estimation via simulation of …rst passage time probabilities for a multidimensional random walk with t distributed increments. This problem is a natural generalization of ruin probabilities in insurance, in which the focus is a one dimensional random walk and captures important features of large deviations for multidimensional heavy-tailed processes. We develop a state-dependent importance sampling estimator for this class of multidimensional problems. Then, we argue, using techniques based on Lyapunov type inequalities that our estimator is strongly e¢ cient.