Linear−quadratic optimal control and nonzero‐sum differential game of forward−backward stochastic system
Linear−quadratic optimal control and nonzero‐sum differential game of forward−backward stochastic system
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DOI：
10.1002/asjc.406
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发表时间：
2012-01
影响因子：
2.4
通讯作者：
Zhiyong Yu
中科院分区：
文献类型：
--
作者：
Zhiyong Yu
在一定的单调性条件下，得到了一类二维正倒向随机微分方程解的存在唯一性结果。然后将这一结果应用于正倒向随机系统的线性-二次型随机最优控制和非零和微分对策。分别给出了最优控制和纳什平衡点的显式表达式。我们注意到我们的方法在研究纳什均衡点的唯一性方面是有效的。
An existence and uniqueness result for one kind of forward–backward stochastic differential equations with double dimensions was obtained under some monotonicity conditions. Then this result was applied to the linear‐quadratic stochastic optimal control and nonzero‐sum differential game of forward–backward stochastic system. The explicit forms of the optimal control and the Nash equilibrium point are obtained respectively. We note that our method is effective in studying the uniqueness of Nash equilibrium point.