Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities

Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities

Hock Peng Chan and Tze Leung Lai

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

Abstract

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.

Primary Subjects: 60F10, 65C05

Secondary Subjects: 60J05, 65C40

Keywords: Boundary crossing probability; importance sampling; Markov additive process; regeneration

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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1174323253
Digital Object Identifier: doi:10.1214/105051606000000664
Mathematical Reviews number (MathSciNet): MR2308332
Zentralblatt MATH identifier: 1134.65005

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