How can the dual martingale help solving the primal optimal stopping problem?

TL;DR

This paper explores how dual martingales can enhance the efficiency of solving primal optimal stopping problems by reducing variance through accurate approximations, supported by numerical examples.

Contribution

It demonstrates that approximating dual martingales can significantly improve primal solution methods for optimal stopping problems.

Findings

Dual martingale approximations reduce variance in primal methods.

Numerical examples confirm efficiency gains from dual martingale approximations.

Improved primal solutions are achieved through dual information.

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.