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