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In this article we propose a Weighted Stochastic Mesh (WSM) Algorithm forapproximating the value of a discrete and continuous time optimal stoppingproblem. We prove that in the discrete case the WSM algorithm leads to  semi-tractability of the corresponding optimal problems in the sense that itscomplexity is bounded in order by $\varepsilon^{-4}\log^{d+2}(1/\varepsilon)$with $d$ being the dimension of the underlying Markov chain. Furthermore westudy the WSM approach in the context of continuous time optimal stoppingproblems and derive the corresponding complexity bounds. Although we can notprove semi-tractability in this case, our bounds turn out to be the tightestones among the bounds known for the existing algorithms in the literature. Weillustrate our theoretical findings by a numerical example.

Semi-tractability of optimal stopping problems via a weighted stochastic mesh algorithm