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根据真人被试的行为金融实验现象,本文构建了描述市场平均投资态度和股票价格的数学模型。首先利用离散动力系统的相关理论研究了模型的稳定性,然后根据金融市场稳定与否对传染效应进行界定。数值模拟发现,在中度传染效应区间内,存在最优传染效应,它能使股票价格以最快速度收敛至均衡价格。在此基础上,进一步探讨了资产结构与股价波动之间的关系。具体而言,在理性传染效应的作用下,当市场中满仓交易者数量与空仓交易者数量相当时,股价呈现小幅水平趋势波动;当满仓交易者数量远高于(低于)空仓交易者数量,股价呈现大幅下跌(上涨)趋势波动。
According to the behavioral financial experiments of live subjects, this paper constructs a mathematical model that describes the average market investment attitude and stock prices. Firstly, the stability of the model is studied by using the relevant theories of discrete dynamical systems, and then the contagion effect is defined according to the stability of financial markets. Numerical simulation shows that there is an optimal contagion effect in the interval of moderate contagion effect, which can make the stock price converge to the equilibrium price as fast as possible. On this basis, we further discuss the relationship between asset structure and stock price volatility. Specifically, under the effect of rational contagion, the stock price fluctuates slightly when the number of full traders in the market equals the number of short traders. When the number of full traders is far above (below) the number of short traders , The stock price showed a sharp drop (rising) trend fluctuations.