英文标题：
《Deep-learning based numerical BSDE method for barrier options》
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作者：
Bing Yu, Xiaojing Xing, and Agus Sudjianto
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最新提交年份：
2019
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英文摘要：
  As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic differential equation (BSDE). We can either solve the PDE to obtain option prices or solve its associated BSDE. Recently a deep learning technique has been applied to solve option prices using the BSDE approach. In this approach, deep learning is used to learn some deterministic functions, which are used in solving the BSDE with terminal conditions. In this paper, we extend the deep-learning technique to solve a PDE with both terminal and boundary conditions. In particular, we will employ the technique to solve barrier options using Brownian motion bridges.
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中文摘要：
众所周知，期权价格是具有终端条件（支付函数）的某个偏微分方程（PDE）的解。偏微分方程的解与倒向随机微分方程（BSDE）的解有着密切的联系。我们可以求解PDE以获得期权价格，也可以求解其相关BSDE。最近，一种深度学习技术被应用于使用BSDE方法求解期权价格。在这种方法中，深度学习用于学习一些确定性函数，这些函数用于求解具有终端条件的盲源分离算法。在本文中，我们将深度学习技术推广到求解具有终端和边界条件的偏微分方程。特别是，我们将使用该技术来解决障碍选项使用布朗运动桥。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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