On the Optimal Design of the Randomized Unbiased Monte Carlo Estimators

26 Pages Posted: 1 May 2019

See all articles by Zhenyu Cui

Zhenyu Cui

Stevens Institute of Technology - School of Business

Chihoon Lee

Stevens Institute of Technology

Lingjiong Zhu

University of Minnesota - Minneapolis

Yunfan Zhu

Stevens Institute of Technology - School of Business

Date Written: March 29, 2019

Abstract

In recent literature, a new class of unbiased Monte Carlo estimators have been proposed, which is based on truncating a telescopic representation of the expectation of a functional of the stochastic process at an independent random level. The generality of the method lies in that it can translate any sequence of asymptotically unbiased estimators into a truly unbiased estimator. However, since any independent truncation level can lead to an unbiased estimator, its optimal choice is crucial for the successful implementation of this unbiased Monte Carlo method in financial engineering applications. We develop a novel efficient algorithm to locate the optimal distribution of the random truncation level in general, which answers positively an open question posted in Rhee and Glynn (2015), and we rigorously establish the convergence and optimality of the algorithm and derive its exact complexity. Our algorithm has a much lower complexity as compared to the literature, and numerical examples confirm our findings. The proposed algorithm is shown to be also applicable to optimization problems arising in contextual areas of supply chain management.

Keywords: simulation optimization, complexity, unbiased estimato, stochastic model applications

JEL Classification: G13, G22

Suggested Citation

Cui, Zhenyu and Lee, Chihoon and Zhu, Lingjiong and Zhu, Yunfan, On the Optimal Design of the Randomized Unbiased Monte Carlo Estimators (March 29, 2019). Stevens Institute of Technology School of Business Research Paper. Available at SSRN: https://ssrn.com/abstract=3362534 or http://dx.doi.org/10.2139/ssrn.3362534

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

Chihoon Lee

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Lingjiong Zhu

University of Minnesota - Minneapolis ( email )

206 Church Street SE
Minneapolis, MN 55455
United States

Yunfan Zhu

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

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