The Annals of Applied Probability

Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities

Hock Peng Chan and Tze Leung Lai

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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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Ann. Appl. Probab., Volume 17, Number 2 (2007), 440-473.

First available in Project Euclid: 19 March 2007

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations 65C05: Monte Carlo methods
Secondary: 60J05: Discrete-time Markov processes on general state spaces 65C40: Computational Markov chains

Boundary crossing probability importance sampling Markov additive process regeneration


Chan, Hock Peng; Lai, Tze Leung. Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities. Ann. Appl. Probab. 17 (2007), no. 2, 440--473. doi:10.1214/105051606000000664.

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