论文标题
两个等效的线性全部完全耦合向后向后的随机微分方程
Two Equivalent Families of Linear Fully Coupled Forward Backward Stochastic Differential Equations
论文作者
论文摘要
在本文中，我们研究了两个完全耦合线性前向后的随机微分方程（FBSDE）的家族。在这些家庭中，可以获得具有完全不同结构的FBSDE的相同适应性。事实证明，第一个FBSD家族相对于统一方法是等效的。因此，如果一个成员存在一个独特的解决方案，就可以得到整个家庭的良好性。通过引入线性变换方法研究了另一个等效的FBSD家族。由于向前和向后方程之间的完全耦合结构，它导致了解决方案的高度相互依存关系。我们能够凭借转换的想法而不会失去良好的态度，从而降低FBSDE的耦合。此外，由于转换矩阵的非分类性，原始FBSDE的解决方案完全由FBSDE溶液在转换后的溶液确定。此外，提出了最佳线性二次（LQ）问题的示例以说明。
In this paper, we investigate two families of fully coupled linear Forward-Backward Stochastic Differential Equations (FBSDE). Within these families, one could get the same well-posedness of FBSDEs with totally different structures. The first family of FBSDEs are proved to be equivalent with respect to the Unified Approach. Thus one could get the well-posedness of the whole family if one member exists a unique solution. Another equivalent family of FBSDEs are investigated by introducing a linear transformation method. By reason of the fully coupling structure between the forward and backward equations, it leads to a highly interdependence in solutions. We are able to lower the coupling of FBSDEs, by virtue of the idea of transformation, without losing the well-posedness. Moreover, owing to the non-degeneracy of the transformation matrix, the solution to original FBSDE is totally determined by solutions of FBSDE after transformation. In addition, an example of optimal Linear Quadratic (LQ) problem is presented to illustrate.
