Pathwise Estimation of Probability Sensitivities Through Terminating or Steady-State Simulations
成果类型：
Article
署名作者：
Hong, L. Jeff; Liu, Guangwu
署名单位：
Hong Kong University of Science & Technology; City University of Hong Kong
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1090.0739
发表日期：
2010
页码：
357-370
关键词：
摘要：
A probability is the expectation of an indicator function. However, the standard pathwise sensitivity estimation approach, which interchanges the differentiation and expectation, cannot be directly applied because the indicator function is discontinuous. In this paper, we design a pathwise sensitivity estimator for probability functions based on a result of Hong [Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57(1) 118-130]. We show that the estimator is consistent and follows a central limit theorem for simulation outputs from both terminating and steady-state simulations, and the optimal rate of convergence of the estimator is n(-2/5) where n is the sample size. We further demonstrate how to use importance sampling to accelerate the rate of convergence of the estimator to n(-1/2), which is the typical rate of convergence for statistical estimation. We illustrate the performances of our estimators and compare them to other well-known estimators through several examples.
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