TY - GEN

T1 - Efficient simulation of light-tailed sums

T2 - 8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2008

AU - Blanchet, Jose H.

AU - Leder, Kevin

AU - Glynn, Peter W.

N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - 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].

AB - 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].

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U2 - 10.1007/978-3-642-04107-5_13

DO - 10.1007/978-3-642-04107-5_13

M3 - Conference contribution

AN - SCOPUS:84904120718

SN - 9783642041068

T3 - Monte Carlo and Quasi-Monte Carlo Methods 2008

SP - 227

EP - 248

BT - Monte Carlo and Quasi-Monte Carlo Methods 2008

PB - Springer Verlag

Y2 - 6 July 2008 through 11 July 2008

ER -