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

Sergio C. Bezerra, Alberto Ohashi, Francys De Souza and 
Francesco Russo
november, 2020
Publication type:
Paper in peer-reviewed journals
Methodology and Computing in Applied Probability, vol. 22, pp. 1221-1255
assets/images/icons/icon_arxiv.png 1707.05250
Keywords :
Optimal stopping; Stochastic Optimal Control; Monte Carlo methods.
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 Leão, 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.
    author={Sergio C. Bezerra and Alberto Ohashi and Francys De Souza and 
           Francesco Russo },
    title={Discrete-type approximations for non-Markovian optimal 
           stopping problems: Part II },
    doi={10.1007/s11009-019-09764-y },
    journal={Methodology and Computing in Applied Probability },
    year={2020 },
    volume={22 },