Backward linear-quadratic stochastic optimal control and nonzero-sum differential game problem with random jumps

被引：0
作者：
Detao Zhang
机构：
[1] Shandong University,School of Mathematics
来源：
Journal of Systems Science and Complexity | 2011年 / 24卷
关键词：
Backward stochastic differential equations; nonzero-sum differential game; optimal control; poisson processes; Riccati equation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps. The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations. The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed. All these results develop those of Lim, Zhou (2001) and Yu, Ji (2008).
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页码：647 / 662
页数：15
相关论文
共 23 条
[1]  
Antonille F.(1993)Backward-forward stochastic differential equations Ann. Appl. Probab. 3 777-793
[2]  
Ma J.(1994)Solving forward-backward stochastic differential equations explicitlya four step scheme Prob. Theory and Related Fields 98 339-359
[3]  
Protter P.(1995)Solutions of forward-backward stochastic differential equations Prob. Theory and Related Fields 103 273-283
[4]  
Yong J.(1999)Fully coupled forward-backward stochastic differential equations and applications to optimal control SIAM J. Control Optim. 37 825-843
[5]  
Hu Y.(1997)Finding adapted solutions of forward-backward stochastic differential equations: Method of continuation Probab. Theory and Relat. Fields 107 537-572
[6]  
Peng S.(1994)Necessary condition for optimal control of stochastic systems with random jumps SIAM J. Control Optim. 32 1447-1475
[7]  
Peng S.(1999)Forward-backward stochastic differential equations with Brownian motion and poisson process Acta Mathematicate Applicatae Sinica 15 433-443
[8]  
Wu Z.(2001)Linear-quadratic control of backward stochastic differential equations SIAM J. Control Optim. 40 450-474
[9]  
Yong J.(1999)Nonzero sum linear-quadratic stochastic differential games and backward-forward equations Stochastic Anal. appl. 17 117-130
[10]  
Tang S.(2005)Forward-backward stochastic differential equations, linear quadratic stochastic optimal control and nonzero sum differential games Journal of Systems Science & Complexity 18 179-192
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