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. We prove the MUSE has finite variance, finite computational complexity, and achieves $\epsilon$-accuracy with $O(1/\epsilon^2)$ computational cost under mild conditions. We demonstrate MUSE empirically in an option pricing problem involving a high-dimensional input and the use of many parallel processors.

翻译：我们提出一个新的公正估算标准,用于估计最佳制止问题的效用。MUSE是多级无偏见制止模拟器的简称,MUSE以向后递转的方式在最佳制止问题的每个阶段构建了不带偏见的多层次蒙特卡洛(MLMC)估计器。与传统的顺序方法不同,MUSE可以平行实施。我们证明MUSE有有限的差异、有限的计算复杂性,并在温和条件下以O(1/\epsilon ⁇ 2)美元计算成本实现超标准美元精确度。我们在涉及高维投入和使用许多平行处理器的选项定价问题中以经验方式展示了MUSE。