An Optimal Stopping Problem of Detecting Entry Points for Trading Modeled by Geometric Brownian Motion

A “buy low, sell high” trading practice is modeled as an optimal stopping problem in this paper. Because its award function lacks sufficient smoothness, traditional free-boundary approach with solution in form of integral equations is not available. Therefore, we design a backward recursive algorithm computing the value function to determine the stopping boundary. Besides, a new PDE technique is developed to conclude the special cases with positive drift. Finally, groups of comparison tests are designed to investigate the model parameters setting as well as the feasibility and profitability of the trading strategy.