English

Discrete-type approximations for non-Markovian optimal stopping problems: Part II

Computational Finance 2019-12-05 v4 Probability

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 Le\~ao, Ohashi and Russo 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.

Keywords

Cite

@article{arxiv.1707.05250,
  title  = {Discrete-type approximations for non-Markovian optimal stopping problems: Part II},
  author = {Sérgio C. Bezerra and Alberto Ohashi and Francesco Russo and Francys de Souza},
  journal= {arXiv preprint arXiv:1707.05250},
  year   = {2019}
}

Comments

Version to appear in Methodology & Computing in Applied Probability

R2 v1 2026-06-22T20:49:17.924Z