媒体影响下的双层投资者行为传染模型研究  

A Study of the Two-Layer Investor Behavior Contagion Model under Media Influence

作　　者：赵文婷 李婷 邵研 Zhao Wenting;Li Ting;Shao Yan(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《宁夏大学学报（自然科学版）》2024年第4期350-360,共11页Journal of Ningxia University(Natural Science Edition)

基　　金：宁夏自然科学基金资助项目(2021AAC03022);国家自然科学基金资助项目(72461029)。

摘　　要：为了讨论正(负)面媒体对股票市场中机构投资者和个人投资者投资行为的影响,将媒体作为与时间有关的状态变量,构建媒体影响下的双层投资者行为传染模型.证明了模型解的正性和有界性,推导了模型的平衡点,通过下一代矩阵法计算传染阈值.利用Routh-Hurwitz准则证明了模型非零平衡点的局部渐近稳定性.通过数值模拟验证了股票市场中投资者行为传染在一定条件下趋于稳定状态,对传染阈值进行敏感性分析,发现媒体的耗散率和正负面媒体的报道强度会影响投资者的投资行为.In order to discuss the influence of positive and negative media on the investment behavior of institutional and individual investors in the stock market,this paper constructs a two-layer investor behavior contagion model in which the media is treated as a time-dependent state variable.The existence of a positive solution of the model is proved.The equilibrium point of the model is derived,and the contagion threshold is calculated using the next generation matrix method.By using the Routh-Hurwitz criterion,the local asymptotic stability of the non-zero equilibrium point of the model is proved.Through the numerical simulation,it is verified that the investor behavior contagion in the stock market tends to a stable state under certain conditions,and the sensitivity of the contagion threshold is analyzed.It is found that the media decay rate and the intensity of positive and negative media coverage will affect the investors'investment behavior.

关 键 词：个人投资者 机构投资者 媒体 稳定性 股票市场 

分 类 号：F830.91[经济管理—金融学] G206[文化科学—传播学]