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arXiv · 1707.05234

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

Dorival Leão·Alberto Ohashi·Francesco Russo
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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 $ε$-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.

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Dorival Leão, Alberto Ohashi, Francesco Russo. 2019-06-21. Discrete-type approximations for non-Markovian optimal stopping problems: Part I. https://arxiv.org/abs/1707.05234

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