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

Dorival Leao, Alberto Ohashi and Francesco Russo
april, 2019
Publication type:
Paper in peer-reviewed journals
Journal of Applied Probability, vol. 56, pp. 981-1005
assets/images/icons/icon_arxiv.png 1707.05234
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.
    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 },
    volume={56 },