The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 17, Number 2 (2007), 440-473.
Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities
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.
Ann. Appl. Probab., Volume 17, Number 2 (2007), 440-473.
First available in Project Euclid: 19 March 2007
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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. https://projecteuclid.org/euclid.aoap/1174323253