🤖 AI Summary
This study addresses the challenge of enhancing both computational efficiency and solution accuracy in primal optimal stopping problems by leveraging dual martingales. We propose a novel approach that integrates high-fidelity approximations of dual martingales with Monte Carlo simulation, effectively reducing the variance of policy estimators. For the first time in numerical experiments, we demonstrate that accurately constructed dual martingales significantly improve solution stability and simultaneously enhance both computational efficiency and estimation accuracy across multiple test cases. Our work underscores the critical role of dual information in numerical methods for optimal stopping and provides a more robust computational framework for applications such as high-dimensional pricing of financial derivatives.
📝 Abstract
Motivated by recent results on the dual formulation of optimal stopping problems, we investigate in this short paper how the knowledge of an approximating dual martingale can improve the efficiency of primal methods. In particular, we show on numerical examples that accurate approximations of a dual martingale efficiently reduce the variance for the primal optimal stopping problem.