Efficient simulation for large deviation probabilities of sums of heavy-tailed increments

Authors:
Jose H. Blanchet;Jingchen Liu
Affiliations:
Harvard University, Cambridge, MA;Harvard University, Cambridge, MA
Venue:
Proceedings of the 38th conference on Winter simulation
Year:
2006

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Introduction to Rare Event Simulation

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Abstract

Let (Xn: n ≥ 0) be a sequence of iid rv's with mean zero and finite variance. We describe an efficient state-dependent importance sampling algorithm for estimating the tail of Sn = X1 + … + Xn in a large deviations framework as n ↗ ∞. Our algorithm can be shown to be strongly efficient basically throughout the whole large deviations region as n ↗ ∞ (in particular, for probabilities of the form P (Sn kn) as k 0). The techniques combine results of the theory of large deviations for sums of regularly varying distributions and the basic ideas can be applied to other rare-event simulation problems involving both light and heavy-tailed features.