Theory of Forward Backward Stochastic Differential Equations and Its Applications

In this paper, based on the basic theory and application background of stochastic differential equation and backward stochastic differential equation, and combined with stochastic optimal control theory and option price theory in financial market, we will derive the general form of fully coupled forward backward stochastic differential equations (FBSDEs in short). From the point of view of the solvability of this kind of equations, the existing methodology in the literature are analyzed and discussed, a ``unified framework'' approach is introduced to guarantee the existence and uniqueness of solutions for non-Markovian FBSDEs, and several further properties of FBSDEs are obtained. A linear transformation method in virtue of the non-degeneracy of transformation matrix is introduced for cases that the linear FBSDEs, as an important supplement and improvement of the ``unified approach'' method, which makes the application of FBSDEs more extensive.