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

Paper: arXiv 2602.09950

Authors: Aurélien Alfonsi, Ahmed Kebaier, Jérôme Lelong

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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a clever synthesis of dual martingale representations with primal optimal stopping frameworks (Longstaff-Schwartz) to achieve significant variance reduction. Empirical demonstrations on Bermudan options are effective, though the presented theoretical derivations rely heavily on previous groundwork by the authors.

Research Flowchart

  flowchart TD
    A["Research Goal: Improve primal optimal stopping efficiency using dual martingales"] --> B["Input: Multi-asset market data & stopping problem parameters"]
    B --> C["Compute approximating dual martingale"]
    C --> D["Apply dual martingale as control variate in primal simulations"]
    D --> E["Execute numerical optimization & Monte Carlo simulation"]
    E --> F["Key Outcome: Significant variance reduction & improved primal estimates"]