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Discrete-type Approximations for Non-Markovian Optimal Stopping Problems: Part II

Author

Listed:
  • Sérgio C. Bezerra

    (Universidade Federal da Paraíba, Rua dos Escoteiros)

  • Alberto Ohashi

    (Universidade de Brasília)

  • Francesco Russo

    (Unité de Mathématiques Appliquées)

  • Francys Souza

    (Universidade de Campinas)

Abstract

In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Leão et al. (??2019) and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartingale state processes such as functionals of path-dependent stochastic differential equations and fractional Brownian motions. Based on statistical learning theory techniques, we provide overall error estimates in terms of concrete approximation architecture spaces with finite Vapnik-Chervonenkis dimension. Analytical properties of continuation values for path-dependent SDEs and concrete linear architecture approximating spaces are also discussed.

Suggested Citation

  • Sérgio C. Bezerra & Alberto Ohashi & Francesco Russo & Francys Souza, 2020. "Discrete-type Approximations for Non-Markovian Optimal Stopping Problems: Part II," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1221-1255, September.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09764-y
    DOI: 10.1007/s11009-019-09764-y
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    References listed on IDEAS

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    1. Dorival Le~ao & Alberto Ohashi & Francesco Russo, 2017. "Discrete-type approximations for non-Markovian optimal stopping problems: Part I," Papers 1707.05234, arXiv.org, revised Jun 2019.
    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.
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    7. Daniel Z. Zanger, 2018. "Convergence Of A Least†Squares Monte Carlo Algorithm For American Option Pricing With Dependent Sample Data," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 447-479, January.
    8. S'ergio C. Bezerra & Alberto Ohashi & Francesco Russo & Francys de Souza, 2017. "Discrete-type approximations for non-Markovian optimal stopping problems: Part II," Papers 1707.05250, arXiv.org, revised Dec 2019.
    9. 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.
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    11. Denis Belomestny & John Schoenmakers & Fabian Dickmann, 2013. "Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 17(4), pages 717-742, October.
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    Cited by:

    1. Bradley Sturt, 2021. "A nonparametric algorithm for optimal stopping based on robust optimization," Papers 2103.03300, arXiv.org, revised Mar 2023.

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