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arXiv · 1707.05250

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

Sérgio C. Bezerra·Alberto Ohashi·Francesco Russo·Francys de Souza
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Abstract

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 Le\~ao, 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.

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Sérgio C. Bezerra, Alberto Ohashi, Francesco Russo, Francys de Souza. 2017-07-17. Discrete-type approximations for non-Markovian optimal stopping problems: Part II. https://arxiv.org/abs/1707.05250

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