Randomized Dimension Reduction for Monte Carlo Simulations

• 成果类型: Article
• 署名作者: Kahale, Nabil
• 署名单位: heSam Universite; ESCP Business School
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2018.3250
• 发表日期: 2020
• 页码: 1421-1439
• 关键词: dimension reduction; variance reduction; effective dimension; Markov chains; Monte Carlo methods

摘要

We present a new unbiased algorithm that estimates the expected value of f(U) via Monte Carlo simulation, where U is a vector of d independent random variables, and f is a function of d variables. We assume that f does not equally depend on all its arguments. Under certain conditions, we prove that, for the same computational cost, the variance of our estimator is lower than the variance of the standard Monte Carlo estimator by a factor of order d. Our method can be used to obtain a low-variance unbiased estimator for the expectation of a function of the state of a Markov chain at a given time step. We study applications to volatility forecasting and time-varying queues. Numerical experiments show that our algorithm dramatically improves on the standard Monte Carlo method for large values of d and is highly resilient to discontinuities.