一类不定仿线性二次型随机微分博弈的鞍点均衡策略

摘要

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 lto'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 e-quilibrium 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.%研究了一类连续时间不定仿线性二次型随机微分博弈的鞍点均衡问题,在It(o)微分的意义下,通过引入一个广义Riccati微分方程(GRDE),证明了该GRDE的可解性是相应随机微分博弈问题均衡策略存在的一个充分必要条件,同时给出了最优策略闭环形式的显式解以及最优性能指标值,所得的结论拓展了已有的有关确定性微分博弈和权系数矩阵正定情形下的随机微分博弈的结果.