Efficient rare-event simulation for perpetuities

Jose Blanchet, Henry Lam and Bert Zwart

Stochastic Processes and their Applications, 2012, vol. 122, issue 10, 3361-3392

Abstract: We consider perpetuities of the form D=B1exp(Y1)+B2exp(Y1+Y2)+⋯, 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.

Keywords: State-dependent importance sampling; Perpetuities; Tail asymptotics; Lyapunov inequalities; Markov chains (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:10:p:3361-3392

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DOI: 10.1016/j.spa.2012.05.002

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