论文标题
一种解决延迟前向和向后随机微分方程的新方法
A New Approach for Solving Delayed Forward and Backward Stochastic Differential Equations
论文作者
论文摘要
本文涉及延迟线性前向后的随机微分方程（D-FBSDE）的脱钩，这比由于延迟引起的无限尺寸而涉及的无延迟情况要多得多。提出了一种新的“离散化”方法，以获得对D-FBSDE的明确解决方案。首先，我们通过使用离散化将连续的时间D-FBSDE转换为离散时间。其次，我们通过应用向后迭代诱导来得出离散时间D-FBSDE的解。最后，通过将离散时间形式的解决方案限制来获得连续时间D-FBSDE的显式解决方案。提出的方法可以应用于延迟求解更通用的FBSDE，这将为随机LQ控制提供完整的解决方案，并随时间延迟。
This paper is concerned with the decoupling of delayed linear forward-backward stochastic differential equations (D-FBSDEs), which is much more involved than the delay-free case due to the infinite dimension caused by the delay. A new approach of `discretization' is proposed to obtain the explicit solution to the D-FBSDEs. Firstly, we transform the continuous-time D-FBSDEs into the discrete-time form by using discretization. Secondly, we derive the solution of the discrete-time D-FBSDEs by applying backward iterative induction. Finally the explicit solution of the continuous-time D-FBSDEs is obtained by taking the limit to the solution of discrete-time form. The proposed approach can be applied to solve more general FBSDEs with delay, which would provide a complete solution to the stochastic LQ control with time delay.
