Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities

• 成果类型: Article
• 署名作者: Chan, Hock Peng; Lai, Tze Leung
• 署名单位: National University of Singapore; Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000664
• 发表日期: 2007
• 页码: 440-473
• 关键词: markov additive processes; Large deviations theory; crossing probabilities; chains; approximations; simulation; tests

摘要

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.