英文标题：
《Discrete-type approximations for non-Markovian optimal stopping
problems: Part I》
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作者：
Dorival Le\\~ao, Alberto Ohashi and Francesco Russo
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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 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 $\\epsilon$-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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中文摘要：
本文提出了一种基于完全非马尔可夫连续过程的离散型近似格式来求解连续时间最优停止问题，该过程适用于布朗运动过滤。这些近似满足适当的变分不等式，使我们能够构造$\\ε$-最优停止时间和完全通用的最优值。基于分数布朗运动驱动的路径依赖型随机微分方程的报酬泛函，给出了最优值的显式收敛速度。特别是，该方法允许我们为非马尔可夫最优停止时间问题设计具体的蒙特卡罗方案，如Bezerra、Ohashi和Russo的配套论文所示。
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分类信息：

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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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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