英文标题：
《Discrete-type approximations for non-Markovian optimal stopping
  problems: Part II》
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作者：
S\\\'ergio C. Bezerra, Alberto Ohashi, Francesco Russo and Francys de
  Souza
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最新提交年份：
2019
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英文摘要：
  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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中文摘要：
本文提出了一种基于布朗运动滤波的Longstaff-Schwartz型最优停止时间算法。该算法基于Le \\~ao、Ohashi和Russo，与之前的工作相比，我们的方法适用于完全非马尔可夫和非半鞅状态过程的最优停止问题，如路径相关随机微分方程和分数布朗运动的泛函。基于统计学习理论技术，我们给出了有限Vapnik-Chervonenkis维数的具体近似体系结构空间的总体误差估计。还讨论了路径相关SDE和具体线性结构近似空间的连续值的分析性质。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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