Journal of Guangdong University of Technology ›› 2012, Vol. 29 ›› Issue (3): 35-38.doi: 10.3969/j.issn.1007-7162.2012.03.006

• Comprehensive Studies • Previous Articles     Next Articles

Saddlepoint Equilibrium Strategy for a Class of Indefinite Affinequadratic Stochastic Differential Games

Zhu Huainian1, Zhang Chengke2, Li Yunlong1, Yang Chaojin1   

  1. 1. School of Management; 2. School of Economics & Commence, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2012-02-21 Online:2012-09-20 Published:2012-09-20

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Abstract: It discusses the saddlepoint equilibrium strategy for indefinite affinequadratic stochastic differential games in continuous time. By introducing a generalized Riccati differential equation (GRDE), it proves that under the condition of Its differential rule, the solvability of GRDE is both the sufficient and necessary condition for the existence of equilibrium strategies. Meanwhile, the explicit solution of equilibrium strategies with closed forms and the optimal value of cost function are obtained. The results expand the previous results of the ordinary deterministic differential games and stochastic differential games with definite weight cost matrices.

Key words: stochastic differential games; saddlepoint equilibrium; generalized Riccati differential equation

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