Unbiased Optimal Stopping via the MUSE

TL;DR

The paper introduces MUSE, a parallelizable unbiased estimator for optimal stopping problems that achieves finite variance and computational complexity, demonstrated in high-dimensional option pricing.

Contribution

It presents MUSE, a novel unbiased estimator for optimal stopping that can be implemented in parallel and guarantees finite variance and complexity.

Findings

MUSE achieves $ ext{O}(1/ extepsilon^2)$ computational cost.

MUSE has finite variance and finite computational complexity.

Empirical validation in high-dimensional option pricing.

Abstract

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.