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Optimal stopping is a fundamental class of stochastic dynamic optimizationproblems with numerous applications in finance and operations management. Weintroduce a new approach for solving computationally-demanding stochasticoptimal stopping problems with known probability distributions. The approachuses simulation to construct a robust optimization problem that approximatesthe stochastic optimal stopping problem to any arbitrary accuracy; we thensolve the robust optimization problem to obtain near-optimal Markovian stoppingrules for the stochastic optimal stopping problem.  In this paper, we focus on designing algorithms for solving the robustoptimization problems that approximate the stochastic optimal stoppingproblems. These robust optimization problems are challenging to solve becausethey require optimizing over the infinite-dimensional space of all Markovianstopping rules. We overcome this challenge by characterizing the structure ofoptimal Markovian stopping rules for the robust optimization problems. Inparticular, we show that optimal Markovian stopping rules for the robustoptimization problems have a structure that is surprisingly simple andfinite-dimensional. We leverage this structure to develop an exactreformulation of the robust optimization problem as a zero-one bilinear programover totally unimodular constraints. We show that the bilinear program can besolved in polynomial time in special cases, establish computational complexityresults for general cases, and develop polynomial-time heuristics by relatingthe bilinear program to the maximal closure problem from graph theory.Numerical experiments demonstrate that our algorithms for solving the robustoptimization problems are practical and can outperform state-of-the-artsimulation-based algorithms in the context of widely-studied stochastic optimalstopping problems from high-dimensional option pricing.

A nonparametric algorithm for optimal stopping based on robust optimization