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Randomized optimal stopping algorithms and their convergence analysis

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  • Christian Bayer
  • Denis Belomestny
  • Paul Hager
  • Paolo Pigato
  • John Schoenmakers

Abstract

In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimisation algorithms. In particular we prove the convergence of the proposed algorithms and derive the corresponding convergence rates.

Suggested Citation

  • Christian Bayer & Denis Belomestny & Paul Hager & Paolo Pigato & John Schoenmakers, 2020. "Randomized optimal stopping algorithms and their convergence analysis," Papers 2002.00816, arXiv.org.
    • Handle: RePEc:arx:papers:2002.00816
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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. 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.
    4. Denis Belomestny & John Schoenmakers, 2018. "Advanced Simulation-Based Methods for Optimal Stopping and Control," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-137-03351-2, October.
    5. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    6. Anastasia Kolodko & John Schoenmakers, 2006. "Iterative construction of the optimal Bermudan stopping time," Finance and Stochastics, Springer, vol. 10(1), pages 27-49, January.
    7. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    8. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    9. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    10. 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.
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