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April 2007 Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities
Hock Peng Chan, Tze Leung Lai
Ann. Appl. Probab. 17(2): 440-473 (April 2007). DOI: 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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Hock Peng Chan. Tze Leung Lai. "Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities." Ann. Appl. Probab. 17 (2) 440 - 473, April 2007.


Published: April 2007
First available in Project Euclid: 19 March 2007

zbMATH: 1134.65005
MathSciNet: MR2308332
Digital Object Identifier: 10.1214/105051606000000664

Primary: 60F10 , 65C05
Secondary: 60J05 , 65C40

Keywords: boundary crossing probability , importance sampling , Markov additive process , regeneration

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.17 • No. 2 • April 2007
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