A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications
Hasib Uddin Molla, Ankit Banarjee, Matthew Backhouse, Jinniao Qiu
在这项工作中,我们将基于深度学习的数值方法扩展到非马尔可维框架内完全耦合的向前向后微分方程(FBSDE)。 提供误差估计和收敛。 与现有的文献相反,我们的方法不仅分析了非马尔可维的框架,而且还解决了完全耦合的设置,其中前进过程的漂移和扩散系数可能是随机的,并且依赖于向后组件Y和Z。 此外,我们通过解决粗糙波动下的实用最大化问题来说明我们框架的实际适用性,这些问题通过拟议的基于深度学习的方法以数字方式解决。
In this work, we extend deep learning-based numerical methods to fully coupled forward-backward stochastic differential equations (FBSDEs) within a non-Markovian framework. Error estimates and convergence are provided. In contrast to the existing literature, our approach not only analyzes the non-Markovian framework but also addresses fully coupled settings, in which both the drift and diffusion coefficients of the forward process may be random and depend on the backward components Y and Z. Furt...
