连续内部交易完美竞争的信息协议古诺均衡  

Cournot equilibrium with information protocol of perfect competition in continuous-time insider trading

作　　者：聂启红 周永辉 NIE Qihong;ZHOU Yonghui(School of Mathematical Sciences,Guizhou Normal University,Guiyang 5500025,China;School of Big Data and Computer Science,Guizhou Normal University,Guiyang 5500025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025 [2]贵州师范大学大数据与计算机科学学院,贵州贵阳550025

出　　处：《纯粹数学与应用数学》2023年第3期350-360,共11页Pure and Applied Mathematics

基　　金：贵州省科技计划项目(黔科中引地[2022]4055,黔科合平台人才[2018]5769);国家自然科学基金(11861025);贵州省教育厅自然科学研究资助项目(黔教技[2023]011)。

摘　　要：对一类拥有风险资产完美信息的两个内部人在连续时间内竞争的市场模型,引入了半强有效性定价下的信息协议古诺均衡.利用滤波理论和极大值原理,探讨了不同协议下的古诺均衡的存在性,给出了所存在均衡的闭式解,以及相应的期望利润,剩余信息,市场流动参数等市场特征,并证明了最优信息协议古诺均衡的存在唯一性.研究表明,双方在选择交易策略时只能释放部分信息,才能达到古诺均衡以实现正的最大化收益;否则,如果不释放信息或完全释放共同的私有信息,则都不存在这种均衡.For a model of insider trading in which two insiders with perfect information on a risky asset compete with each other in continuous time,a concept of Cournot equilibrium with information protocol under semi-strong efficient pricing is introduced.With the help of filtering theory and maximum principle,the existence of such equilibrium is discussed,and a closed form of the existing equilibrium with its market characteristics including expected profit,residual information and market liquidity is also given;accordingly,the existence and uniqueness of Cournot equilibrium with the best information protocol is proved.It shows that each of the two insiders can only release partial information of their perfect information when choosing trading strategy,so as to achieve equilibrium and earn a positive maximal profit;otherwise,there is no such equilibrium,if the common private information is not released or completely released.

关 键 词：连续内部交易 完美竞争 滤波理论 信息协议古诺均衡 极大值原理 

分 类 号：O211.6[理学—概率论与数理统计] O211.9[理学—数学]