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.
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 -