摘要
This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different ways.As a consequence,the open problems raised by Chen and Yong(2007) are solved.To characterize the saddle points more clearly,coupled forward-backward stochastic Volterra integral equations and stochastic Fredholm-Volterra integral equations are introduced.Compared with deterministic game problems,some new terms arising from the procedure of deriving the later equations reflect well the essential nature of stochastic systems.Moreover,our representations and arguments are even new in the classical SDEs case.
This paper studies linear quadratic games problem for stochastic Volterra integral equations （SVIEs in short） where necessary and sufficient conditions for the existence of saddle points are derived in two different ways. As a consequence, the open problems raised by Chen and Yong （2007） are solved. To characterize the saddle points more clearly, coupled forward-backward stochastic Volterra integral equations and stochastic Fredholm-Volterra integral equations are introduced. Compared with deterministic game problems, some new terms arising from the procedure of deriving the later equations reflect well the essential nature of stochastic systems. Moreover, our representations and arguments are even new in the classical SDEs case.
基金
supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002)
National Natural Science Foundation of China(Grant Nos.11231007,11301298,11471231,11401404,11371226,11071145 and 11231005)
China Postdoctoral Science Foundation(Grant No.2014M562321)
Foundation for Innovative Research Groups of National Natural Science Foundation of China(Grant No.11221061)
the Program for Introducing Talents of Discipline to Universities(the National 111Project of China's Higher Education)(Grant No.B12023)
关键词
线性二次型
随机积分
VOLTERRA积分方程
FREDHOLM积分方程
游戏
推导方法
充要条件
博弈问题
stochastic integral games, backward stochastic Volterra integral equations, stochastic Fredholm-Volterra integral equations, saddle points, linear quadratic optimal control problems
