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A Type of General Forward-Backward Stochastic Differential Equations and Applications |
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| Authors: | Li CHEN and Zhen WU |
| Institution: | [1]Department of Mathematics, China University of Mining and Technology, Beijing 100083, China [2]Corresponding author. School of Mathematics, Shandong University, Jinan 250100, China |
| Abstract: | The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations. The existence and uniqueness results of the general FBSDEs are obtained. In the framework of the general FBSDEs in this paper, the explicit form of the optimal control for linearquadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained. |
| Keywords: | Stochastic delayed differential equations Anticipated backward stochastic differential equations Forward-backward stochastic differential equations Linear-quadratic stochastic optimal control with delay Nonzero sum stochastic differential game with delay |
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