Efficient rare-event simulation for perpetuities

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Blanchet, Jose¹  Lam, Henry² 

[1] Columbia Univ, Dept Ind Engn & Operat Res, New York, NY 10027 USA

[2] Boston Univ, Dept Math & Stat, Boston, MA 02215 USA

关键词: State-dependent importance sampling;    Perpetuities;    Tail asymptotics;    Lyapunov inequalities;    Markov chains;   

DOI  :  10.1016/j.spa.2012.05.002

来源: Elsevier

【 摘 要 】

We consider perpetuities of the form D = B-1 exp (Y-1) + B-2 exp (Y-1 + Y-2) + . . . , where the Y-j's and B-j's might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the Y-j's satisfy the so-called Cramer condition with associated root theta(*) is an element of (0, infinity) and that the tails of the B-j's are appropriately behaved so that D is regularly varying with index theta(*). We illustrate by means of an example that the natural state-independent importance sampling estimator obtained by exponentially tilting the Y-j's according to theta(*) 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. (C) 2012 Published by Elsevier B.V.

【 授权许可】

Free