Optimal Stopping Rule for a Project with Uncertain Completion Time and Partial Salvageability

Abstract

In this paper, we developed an optimal stopping model for the control of an investment project that takes an uncertain length of time to develop and can still provide a partial payoff even if it is terminated without achieving its original performance objectives. We first investigated the solution of the model under a specific set of assumptions about the forms of the functions that characterize the uncertainty about the project and the buildup of its value. An analytical solution was derived for the special case where the discount rate is zero, and numerical solutions were obtained for the general case where the discount rate is allowed to be positive. Using the insights from the solution under the specific set of assumptions, we then examined the solutions of the model under alternative assumptions about those component functions. Our results suggest that the optimal control policy is quite sensitive to how the terminal payoff evolves in a project’s development process, pointing to the importance of carefully accounting for its impact in determining the control policy for this kind of project. Finally, we also suggested methods for estimating the forms of the component functions that characterize the uncertainty about the project and the buildup of its value.