The Expected Hitting Time Approach to Optimal Price Adjustment Problems

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