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

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Listed:
  • Aur'elien Alfonsi
  • Ahmed Kebaier
  • J'er^ome 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.

Suggested Citation

  • Aur'elien Alfonsi & Ahmed Kebaier & J'er^ome Lelong, 2026. "How can the dual martingale help solving the primal optimal stopping problem?," Papers 2602.09950, arXiv.org.
    • Handle: RePEc:arx:papers:2602.09950
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    File URL: http://arxiv.org/pdf/2602.09950
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    References listed on IDEAS

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    2. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    3. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    4. J'er^ome Lelong, 2019. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Papers 1901.05672, arXiv.org, revised Jul 2020.
    5. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    6. Jérôme Lelong, 2018. "Dual pricing of American options by Wiener chaos expansion," Post-Print hal-01299819, HAL.
    7. Aurélien Alfonsi & Ahmed Kebaier & Jérôme Lelong, 2025. "A pure dual approach for hedging Bermudan options," Post-Print hal-04563713, HAL.
    8. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
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    10. Vijay V. Desai & Vivek F. Farias & Ciamac C. Moallemi, 2012. "Pathwise Optimization for Optimal Stopping Problems," Management Science, INFORMS, vol. 58(12), pages 2292-2308, December.
    11. Jérôme Lelong, 2020. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Post-Print hal-01983115, HAL.
    12. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    13. Aurélien Alfonsi & Ahmed Kebaier & Jérôme Lelong, 2025. "A Pure Dual Approach for Hedging Bermudan Options," Mathematical Finance, Wiley Blackwell, vol. 35(4), pages 745-759, October.
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