Unbiased Optimal Stopping via the MUSE

We propose a new unbiased estimator for estimating the utility of the optimal stopping problem. The MUSE, short for `Multilevel Unbiased Stopping Estimator, constructs the unbiased Multilevel Monte Carlo (MLMC) estimator at every stage of the optimal stopping problem in a backward recursive way. In contrast to traditional sequential methods, the MUSE can be implemented in parallel when multiple processors are available. We prove the MUSE has finite variance, finite computational complexity, and achieves $varepsilon$-accuracy with $O(1/varepsilon^2)$ computational cost under mild conditions. We demonstrate MUSE empirically in several numerical examples, including an option pricing problem with high-dimensional inputs, which illustrates the use of the MUSE on computer clusters.