Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities

Details Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities

2007-03-30

arxiv.org/abs/math/0703910v1

Annals of Applied Probability 2007, Vol. 17, No. 2, 440-473

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000664 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000664

Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given examples in which importance sampling measures that are consistent with large deviations can perform much worse than direct Monte Carlo. We address this problem by using certain mixtures of exponentially twisted measures for importance sampling. Their asymptotic optimality is established by using a new class of likelihood ratio martingales and renewal theory.

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