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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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    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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