论文标题
一种深度学习方法，用于依赖路径偏微分方程的概率数值解
A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations
论文作者
论文摘要
最近关于路径依赖性偏微分方程（PPDE）的工作表明，PPDE解决方案可以通过概率代表来近似，该概率表示通过使用回归来估计条件期望。但是，这种方法的限制是需要在功能空间中选择基础。在本文中，我们通过使用深度学习方法来克服这一限制，并表明该设置允许在条件期望的近似情况下推导误差界限。提出了基于两人零和游戏的数值示例，以及亚洲和障碍选项定价。与其他深度学习方法相比，我们的算法似乎更为准确，尤其是在大方面。
Recent work on Path-Dependent Partial Differential Equations (PPDEs) has shown that PPDE solutions can be approximated by a probabilistic representation, implemented in the literature by the estimation of conditional expectations using regression. However, a limitation of this approach is to require the selection of a basis in a function space. In this paper, we overcome this limitation by the use of deep learning methods, and we show that this setting allows for the derivation of error bounds on the approximation of conditional expectations. Numerical examples based on a two-person zero-sum game, as well as on Asian and barrier option pricing, are presented. In comparison with other deep learning approaches, our algorithm appears to be more accurate, especially in large dimensions.
