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Dynamic programming for optimal stopping via pseudo-regression

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  • Christian Bayer
  • Martin Redmann
  • John Schoenmakers

Abstract

We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the least-squares error functional. Coupled with new proposals for simulation of the underlying samples, we call the approach "pseudo regression". A detailed convergence analysis is provided and it is shown that the approach asymptotically leads to less computational cost for a pre-specified error tolerance, hence to lower complexity. The method is justified by numerical examples.

Suggested Citation

  • Christian Bayer & Martin Redmann & John Schoenmakers, 2018. "Dynamic programming for optimal stopping via pseudo-regression," Papers 1808.04725, arXiv.org, revised Apr 2019.
    • Handle: RePEc:arx:papers:1808.04725
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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. 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.
    4. Daniel Zanger, 2013. "Quantitative error estimates for a least-squares Monte Carlo algorithm for American option pricing," Finance and Stochastics, Springer, vol. 17(3), pages 503-534, July.
    5. 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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