Unbiased Estimation with Square Root Convergence for SDE Models

• 成果类型: Article
• 署名作者: Rhee, Chang-Han; Glynn, Peter W.
• 署名单位: University System of Georgia; Georgia Institute of Technology; Stanford University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2015.1404
• 发表日期: 2015
• 页码: 1026-1043
• 关键词: exact simulation; approximation

摘要

In many settings in which Monte Carlo methods are applied, there may be no known algorithm for exactly generating the random object for which an expectation is to be computed. Frequently, however, one can generate arbitrarily close approximations to the random object. We introduce a simple randomization idea for creating unbiased estimators in such a setting based on a sequence of approximations. Applying this idea to computing expectations of path functionals associated with stochastic differential equations (SDEs), we construct finite variance unbiased estimators with a square root convergence rate for a general class of multidimensional SDEs. We then identify the optimal randomization distribution. Numerical experiments with various path functionals of continuous-time processes that often arise in finance illustrate the effectiveness of our new approach.