Optimal Unbiased Estimation for Expected Cumulative Cost

13 Pages Posted: 30 Apr 2018

See all articles by Zhenyu Cui

Zhenyu Cui

Stevens Institute of Technology - School of Business

Michael Fu

University of Maryland - College Park

Yijie Peng

Department of Industrial Engineering and Management, Peking University

Lingjiong Zhu

University of Minnesota - Minneapolis

Date Written: April 11, 2018

Abstract

We consider estimating an expected infinite-horizon cumulative cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the random horizon are given. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. Numerical experiments substantiate the theoretical results.

Keywords: unbiased simulation, optimal control, cumulative cost, efficiency of estimator

JEL Classification: C61, C63

Suggested Citation

Cui, Zhenyu and Fu, Michael and Peng, Yijie and Zhu, Lingjiong, Optimal Unbiased Estimation for Expected Cumulative Cost (April 11, 2018). Stevens Institute of Technology School of Business Research Paper. Available at SSRN: https://ssrn.com/abstract=3161030 or http://dx.doi.org/10.2139/ssrn.3161030

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

Michael Fu

University of Maryland - College Park ( email )

College Park, MD 20742
United States

Yijie Peng

Department of Industrial Engineering and Management, Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

HOME PAGE: http://en.coe.pku.edu.cn/Faculty-A-Z/163.htm

Lingjiong Zhu

University of Minnesota - Minneapolis ( email )

206 Church Street SE
Minneapolis, MN 55455
United States

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