Blanchet, J., Lam, H., & Zwart, B. (2012). Efficient rare-event simulation for perpetuities. Stochastic Processes and Their Applications, 122(10), 3361-3392. https://doi.org/10.1016/j.spa.2012.05.002

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Abstract

We consider perpetuities of the form where the Yj’s and Bj’s might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the Yj’s satisfy the so-called Cramér condition with associated root θ∗∈(0,∞) and that the tails of the Bj’s are appropriately behaved so that D is regularly varying with index θ∗. We illustrate by means of an example that the natural state-independent importance sampling estimator obtained by exponentially tilting the Yj’s according to θ∗ fails to provide an efficient estimator (in the sense of appropriately controlling the relative mean squared error as the tail probability of interest gets smaller). Then, we construct estimators based on state-dependent importance sampling that are rigorously shown to be efficient.

Authors
Jose Blanchet, Henry Lam, Bert Zwart
Publication date
2012/10/1
Journal
Stochastic Processes and their Applications
Volume
122
Issue
10
Pages
3361-3392
Publisher
North-Holland