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

, and
april, 2019
Publication type:
Paper in peer-reviewed journals
Journal:
Journal of Applied Probability, vol. 56, pp. 981-1005
arXiv:
Abstract:
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct $\epsilon$-optimal stopping times and optimal values in full generality. Explicit rates of convergence are presented for optimal values based on reward functionals of path-dependent SDEs driven by fractional Brownian motion. In particular, the methodology allows us to design concrete Monte-Carlo schemes for non-Markovian optimal stopping time problems as demonstrated in the companion paper by Bezerra, Ohashi and Russo.
BibTeX:
@article{Lea-Oha-Rus-2019,
author={Dorival Leao and Alberto Ohashi and Francesco Russo },
title={Discrete-type approximations for non-Markovian optimal
stopping problems: Part I },
doi={10.1017/jpr.2019.57 },
journal={Journal of Applied Probability },
year={2019 },
month={4},
volume={56 },
pages={981--1005},
}