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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。
The connection between the dynamic programming principle and the maximum principle of a fully coupled forward-backward stochastic control system is studied. The recursive utility function is given by the solution of a fully coupled forward-backward stochastic differential equation. The main result is given the relation between the optimal value function, the generalized Hamiltonian function and the dual process under the certain smoothness assumption, but the diffusion term of the forward equation does not contain the variable z. The general result is still open to question. Finally, a linear example is given to explain the theoretical result.