Efficient simulation of light-tailed sums: An old-folk song sung to a faster new tune

Jose H. Blanchet, Kevin Leder, Peter W. Glynn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

We revisit a classical problem in rare-event simulation, namely, efficient estimation of the probability that the sample mean of n independent identically distributed light tailed (i.e. with finite moment generating function in a neighborhood of the origin) random variables lies in a sufficiently regular closed convex set that does not contain their mean. It is well known that the optimal exponential tilting (OET), although logarithmically efficient, is not strongly efficient (typically, the squared coefficient of variation of the estimator grows at rate n1/2). After discussing some important differences between the optimal change of measure and OET (for instance, in the one dimensional case the size of the overshoot is bounded for the optimal importance sampler and of order O(n1/2) for OET) that indicate why OET is not strongly efficient, we provide a state-dependent importance sampling that can be proved to be strongly efficient. Our procedure is obtained based on computing the optimal tilting at each step, which corresponds to the solution of the Isaacs equation studied recently by Dupuis and Wang [8].

Original languageEnglish (US)
Title of host publicationMonte Carlo and Quasi-Monte Carlo Methods 2008
PublisherSpringer Verlag
Pages227-248
Number of pages22
ISBN (Print)9783642041068
DOIs
StatePublished - 2009
Event8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2008 - Montreal, QC, Canada
Duration: Jul 6 2008Jul 11 2008

Publication series

NameMonte Carlo and Quasi-Monte Carlo Methods 2008

Other

Other8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2008
CountryCanada
CityMontreal, QC
Period7/6/087/11/08

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