A nonparametric algorithm for optimal stopping based on robust optimization

Abstract

Optimal stopping is a class of stochastic dynamic optimization problems with applications in finance and operations management. In this paper, we introduce a new method for solving stochastic optimal stopping problems with known probability distributions. First, we use simulation to construct a robust optimization problem that approximates the stochastic optimal stopping problem to any arbitrary accuracy. Second, we characterize the structure of optimal policies for the robust optimization problem, which turn out to be simple and finite-dimensional. Harnessing this characterization, we develop exact and approximation algorithms for solving the robust optimization problem, which in turn yield policies for the stochastic optimal stopping problem. Numerical experiments show that this combination of robust optimization and simulation can find policies that match, and in some cases significantly outperform, those from state-of-the-art algorithms on low-dimensional, non-Markovian optimal stopping problems from options pricing.