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A Monotone Limit Approach to Entropy-Regularized American Options

Author

Listed:
  • Daniel Chee

    (School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia)

  • Noufel Frikha

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Libo Li

    (School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia)

Abstract

Recent advances in continuous-time optimal stopping have been driven by entropy-regularized formulations of randomized stopping problems, with most existing approaches relying on partial differential equation methods. In this paper, we propose a fully probabilistic framework based on the Doob-Meyer-Mertens decomposition of the Snell envelope and its representation through reflected backward stochastic differential equations. We introduce an entropy-regularized penalization scheme yielding a monotone approximation of the value function and establish explicit convergence rates under suitable regularity assumptions. In addition, we develop a policy improvement algorithm based on linear backward stochastic differential equations and illustrate its performance through a simple numerical experiment for an American-style max call option.

Suggested Citation

  • Daniel Chee & Noufel Frikha & Libo Li, 2026. "A Monotone Limit Approach to Entropy-Regularized American Options," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05520656, HAL.
    • Handle: RePEc:hal:cesptp:hal-05520656
    Note: View the original document on HAL open archive server: https://hal.science/hal-05520656v1
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    References listed on IDEAS

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    1. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    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. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2017. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Post-Print hal-01141801, HAL.
    4. Daniel Chee & Noufel Frikha & Libo Li, 2026. "Entropy-regularized penalization schemes for American options and reflected BSDEs with singular generators," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05520660, HAL.
    5. Yijie Huang & Mengge Li & Xiang Yu & Zhou Zhou, 2025. "Continuous-time reinforcement learning for optimal switching over multiple regimes," Papers 2512.04697, arXiv.org, revised Dec 2025.
    6. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen, 2019. "Pricing and hedging American-style options with deep learning," Papers 1912.11060, arXiv.org, revised Jul 2020.
    7. Noufel Frikha & Libo Li & Daniel Chee, 2025. "An Entropy Regularized BSDE Approach to Bermudan Options and Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05265653, HAL.
    8. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen & Timo Welti, 2019. "Solving high-dimensional optimal stopping problems using deep learning," Papers 1908.01602, arXiv.org, revised Aug 2021.
    9. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    10. Yuchao Dong & Harry Zheng, 2025. "Extended HJB Equation for Mean-Variance Stopping Problem: Vanishing Regularization Method," Papers 2510.24128, arXiv.org.
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    Cited by:

    1. Daniel Chee & Noufel Frikha & Libo Li, 2026. "Entropy-regularized penalization schemes for American options and reflected BSDEs with singular generators," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05520660, HAL.
    2. Daniel Chee & Noufel Frikha & Libo Li, 2026. "Entropy-regularized penalization schemes and reflected BSDEs with singular generators," Papers 2602.18078, arXiv.org, revised Mar 2026.

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