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

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.

💡 Research Summary

The paper investigates how an approximated dual martingale can be leveraged to improve the efficiency of primal methods for solving discrete‑time optimal stopping problems, such as the pricing of Bermudan options. The authors start by recalling the classical primal formulation based on the Snell envelope (U_n) and the Longstaff‑Schwartz (LS) regression algorithm, which approximates the continuation value (\mathbb{E}