An Easy-To-Use Toolkit for Solving Optimal Stopping Problems

This paper studies a class of optimal stopping problems that has become popular in the area of investment under uncertainty (``real options''). Necessary conditions for solutions to these problems are that the solution dominates the payoff function and is superharmonic. Neither property is typically verified in the literature. Here, easy-to-check conditions that establish solutions to many optimal stopping problems are provided. Attention is focussed on problems with payoff functions that are monotonic in the state variable (either increasing or decreasing) or payoff functions that are decreasing, then increasing. The state variable can be driven by any one-dimensional time-homogenous diffusion. An application to Bayesian sequential hypothesis testing illustrates the applicability of the approach.