Discrete-type approximations for non-Markovian optimal stopping problems: Part I
april, 2019
Publication type:
Paper in peer-reviewed journals
Journal:
Journal of Applied Probability, vol. 56, pp. 981-1005
DOI:
HAL:
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}, }