关键词: 随机动力系统, 系统动力学, 投资者信念, 投资者情绪

Abstract: For the past years, the volatility of China's stock market has intensified, and the fluctuations of stock prices have not conformed to the traditional definition of a random walk process, but present irrational states, and frequently exhibit anomalous phenomena that are inconsistent with the assumptions of traditional financial theories, such as the “thousands of stocks hitting limit down” in 2015, the “fuse” phenomenon in 2016, and the recent fluctuations in the stock market due to the impact of the epidemic, which has attracted great attention from society. Investors serve as carriers and suppliers of heterogeneous beliefs and investor sentiment, playing a role in information transmission and circulation. Heterogeneous beliefs reflect investors' judgments on future expected situations, while investor sentiment is a reflection of investors' psychology, manifested as sensitivity to information. Therefore, this article re-evaluates the volatility of the stock market based on the theory of systemics, and attempts to apply the theory of complex systems to analyze the impact of rational investors' behavior on stock market volatility from a novel perspective.
　The stock market is studied as an open system, and the interactive impact between heterogeneous beliefs and investor sentiment under the joint effect of external environmental input information and internal factors change is analyzed. Based on individual differences, different types of investors are formed: Irrational investors (completely driven by emotions), limited rational investors (influenced by the other two types of investors), and rational investors. Investors conduct transactions under expected utility, which affects prices, and price changes are then used as initial condition information to enter the next link. The evolution of the stock market system is influenced by a variety of factors, and the interaction relationships between these factors are complex. This article incorporates the entire stock market into a dynamic system, establishes a random dynamic system model, with stock prices as the explicit feature of the system. Based on complexity, it is divided into three levels, and the three types of investors serve as the breakthrough point. As a characteristic,the different degree of rationality of investors, is used to construct a random dynamic system to simulate the evolution process of investors in the market, and to analyze the mutation of its elements and the evolution equilibrium of the system. Based on the Bayesian rules, and the asymptotic response of information flow and noise,there is a mutual transformation relationship among three types of investors, which mainly constitutes three feedback rings. Based on the randomness of investors entering and exiting the market, using the method of random system dynamics, a random dynamical system model has been built. It analyzes correlative influence factors, simulates the dynamic changes of three kinds of investors in the market, and makes an dynamic adjustment to the quantity of the three kinds of investors,in order to reveal the influence of the structure of investors rationality on the fluctuation of the stock market price. The results show that the changes in the rational structure of investors are a dynamic equilibrium process, and investor rationality is not discrete but continuous, with mutual transformation. The existence of irrational investors in the market is also necessary, it can enrich the liquidity of the entire market, enrich the investment levels of the stock market, and enhance the market's activity. The dynamic deduction process of the degree of rationality of the three types of investors in stock market transactions also constitutes an important driving force for the development of the stock market.
　This article will continue to further study the time-varying impact of the changes in investors' rational structure on stock market volatility, and conduct a series of empirical studies to reveal more complex generation mechanisms of influence paths.

Key words: random dynamical system, system dynamical, investor belief, investor sentiments