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

Author

Listed:
  • Aurélien Alfonsi

    (CERMICS UMR 9032 - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - CNRS - Centre National de la Recherche Scientifique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris)

  • Ahmed Kebaier

    (LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Jérôme Lelong

    (DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

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.

Suggested Citation

  • Aurélien Alfonsi & Ahmed Kebaier & Jérôme Lelong, 2026. "How can the dual martingale help solving the primal optimal stopping problem?," Working Papers hal-05504568, HAL.
    • Handle: RePEc:hal:wpaper:hal-05504568
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