The Expected Hitting Time Approach to Optimal Price Adjustment Problems

37 Pages Posted: 2 May 2017  

Yiying Cheng

University of Kansas

Hamed Ghoddusi

Stevens Institute of Technology - School of Business

Yaozhong Hu

University of Kansas

Chihoon Lee

Stevens Institute of Technology

Date Written: April 30, 2017

Abstract

We offer a novel approach for solving optimal price adjustment problems, when the underlying process is a Geometric Brownian Motion (GBM) process. Our approach relies on characterizing the cumulative cost of deviation and the cost of adjusting price until the hitting time of the lower or upper barriers. Using this approach, we are able to derive an analytical expression for the cost function, that does not require solving a PDE or running Monte-Carlo simulations. We apply our framework to the real world problem of adjusting domestic energy prices in countries that adopt administratively-set energy price rules. Our toolbox code in Matlab can be easily modified to be used to calculate optimal policies in a wide range of topics in finance, operations management, economics, and natural resource management.

Keywords: Stochastic Control, Impulse Control, Expected Hitting Time, Price Setting, Energy Subsidies

Suggested Citation

Cheng, Yiying and Ghoddusi, Hamed and Hu, Yaozhong and Lee, Chihoon, The Expected Hitting Time Approach to Optimal Price Adjustment Problems (April 30, 2017). Stevens Institute of Technology School of Business Research Paper. Available at SSRN: https://ssrn.com/abstract=2960852 or http://dx.doi.org/10.2139/ssrn.2960852

Yiying Cheng

University of Kansas ( email )

1415
Lawrence, KS 66045
United States

Hamed Ghoddusi (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://www.ghoddusi.com

Yaozhong Hu

University of Kansas ( email )

1415
Lawrence, KS 66045
United States

Chihoon Lee

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

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