DIFFERENTIAL GAMES OF PARTIAL INFORMATION FORWARD-BACKWARD DOUBLY SDE AND APPLICATIONS ∗
DIFFERENTIAL GAMES OF PARTIAL INFORMATION FORWARD-BACKWARD DOUBLY SDE AND APPLICATIONS ∗
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DOI：
10.1051/cocv/2013055
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
E. Hui;Hua Xiao
中科院分区：
文献类型：
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作者：
E. Hui;Hua Xiao
研究了一类新的正倒向双随机微分方程微分对策问题。有两个显著特征。一个是我们的博弈系统是初始耦合的，而不是终端耦合的。另一个是要求容许控制适应于由潜在布朗运动产生的信息的子集。建立了非零和博弈的平衡点和零和博弈的鞍点的一个必要条件和一个充分条件。为了说明一些可能的应用，一个线性二次非零和微分对策的例子。应用随机滤波技术，我们得到了平衡点的显式表达式。
This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games and a saddle point of zero-sum games. To illustrate some possible applications, an example of linear-quadratic nonzero-sum differential games is worked out. Applying stochastic filtering techniques, we obtain an explicit expression of the equilibrium point.