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Discrete-type Approximations for Non-Markovian Optimal Stopping Problems: Part II

Sérgio C. Bezerra (), Alberto Ohashi (), Francesco Russo () and Francys Souza ()
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Sérgio C. Bezerra: Universidade Federal da Paraíba, Rua dos Escoteiros
Alberto Ohashi: Universidade de Brasília
Francesco Russo: Unité de Mathématiques Appliquées
Francys Souza: Universidade de Campinas

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 3, 1221-1255

Abstract: 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 Leão et al. (??2019) 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.

Keywords: Optimal stopping; Stochastic optimal control; Monte Carlo methods; Primary: 93E20; Secondary: 60H30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09764-y

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