Rare-event simulation for a multidimensional random walk with t distributed increments

Authors:
Jose H. Blanchet;Jingchen Liu
Affiliations:
Harvard University, Cambridge, MA;Harvard University, Cambridge, MA
Venue:
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Year:
2007

Citing 2
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Abstract

We consider the problem of efficient estimation of first passage time probabilities for a multidimensional random walk with t distributed increments, via simulation. In addition of being a natural generalization of the problem of computing ruin probabilities in insurance -- in which the focus is a one dimensional random walk -- this problem captures important features of large deviations for multidimensional heavy-tailed processes (such as the role played by the mean of the random walk in connection to the spatial location of the target set). 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 efficient.