中文摘要：

研究了完全耦合正倒向随机控制系统的动态规划原理和最大值原理之间的联系,其递归效用泛函由受控完全耦合的正倒向随机微分方程的解给出。主要结果是在一定的光滑性假设下,给出了最优值函数、广义哈密顿函数和对偶过程之间的联系,但正向方程的扩散项不含变量z。一般情形的结果仍是公开问题。最后给出一个线性例子来解释理论结果。

英文摘要：

This paper is concerned with the connection between dynamic programming principle (DPP)and maximum principle (MP)for the forward-backward stochastic control system,where the recursive cost functional is defined as one of the solution to a controlled fully coupled forward-backward stochastic differential equation (FBSDE).With some smooth assumptions,relations among the value function,generalized Hamiltonian function and adjoint processes are given,when the diffusion coefficient of the forward equation does not contain the state variable z.The general case for the problem is open.A linear example is discussed as the illustration of our main result.