论文总字数：20001字

摘 要

回顾20世纪以来世界范围内爆发的一系列经济危机，每一次危机都对世界各国产生了不可磨灭的影响，因此各国对股市风险等金融危机蔓延机制的研究都给予了高度的重视，中国也不例外。我国股市多是以散户为主，在散户占据绝对主导的情况下，由于信息的不对称性，市场变得更容易波动，所以我总结了一些散户典型的心理特征：1.过度自信，容易高估自己的投机水平2.规避风险意识较弱，被套时不能够及时止损。3.具有较强的从众心理。个人投资者的情绪常常会表现出不稳定的状态，很容易被动的接收他人情绪或者错误信息的影响，因此可能会轻易改变自己的看法或预期。

在对股市危机研究中，一些学者从类似流行病的视角开展研究，发现这类风险的传播机制确与病毒的传染机制有相同之处，二者均是由个体传染到群体，最终造成大规模的混乱。于是本文通过建立饱和发生率的的动力学模型，也就是传染病SEIR模型，通过借用SEIR模型来模拟股票投资者被信息传染并继续传播的过程，而且国内对于研究股票市场风险传染利用传染病模型进行研究的比较少见，多是运用copula模型以及VAR模型，近期的学者会运用复杂网络理论来进行网络分析，所以本文运用此次模型来研究股市危机也算是本文的一个创新所在。

在充分查找传染病模型以及如何测度股市危机的文献后，我们根据股市的实际情况修改传染病模型，并假设股票市场的信息扩散存在一定的规则，接着我们对其进行数值仿真，解释基本再生数，并通过基本再生数的计算来验证无病平衡点的和地方病平衡点的稳定性并通过引入疾病持续生存的概念，解释基本再生数大于等于1或者小于1的情况下，股市危机的传染过程，验证得到当基本再生数时，股市危机可以完全被消除，接下来用matlab进行进一步的仿真模拟，直观的模拟出股市的风险的扩散过程，以用于检验本文研究的可靠性。最后本文通过结合并分析已有的研究和本文的研究，针对如何控制并降低基本再生数来为管理者及相关部门提出了合适的危机救助策略。

关键词：SEIR模型，股市风险传播机制，无病平衡点，局部稳定性

The application of a dynamic model with saturated incidence in the study of risk contagion mechanism in stock market

Abstract

Looking back on a series of economic crises in the world since the 20th century, each crisis has an indelible impact on all countries in the world. Therefore, all countries attach great importance to the study of the spread mechanism of financial crisis such as stock market risk, and China is no exception. In China, the stock market is mostly dominated by retail investors. Under the condition that retail investors are absolutely dominant, the market becomes more volatile due to the asymmetry of information, so I summarize some typical psychological characteristics of retail investors: 1. Overconfidence, easy to overestimate their level of speculation; 2. Weak awareness of risk aversion, unable to stop loss in time when they are covered. 3. Have a strong herd mentality. Individual investor's emotions often show unstable state, and it is easy to passively receive the influence of other's emotions or wrong information, so it may easily change their own views or expectations.

In the study of the stock market crisis, some scholars carry out research from the perspective of similar epidemic, and find that the transmission mechanism of this kind of risk is indeed the same as that of the virus. Both of them are transmitted from individuals to groups, and eventually cause large-scale chaos. In this paper, we build a dynamic model of saturated incidence, that is, SEIR model of infectious diseases, and use SEIR model to simulate the process that stock investors are infected by information and continue to spread. In China, there are few studies on the use of infectious diseases model to study the risk contagion of stock market. Most of them use copula model and VAR model, which will be used by recent scholars The complex network theory is used to analyze the network, so this paper uses this model to study the stock market crisis is also an innovation of this paper.

After fully searching for the literature of infectious disease model and how to measure the stock market crisis, we modify the infectious disease model according to the actual situation of the stock market, and assume that there are certain rules for the information diffusion of the stock market, then we carry out numerical simulation on it, explain the basic regeneration number, and verify the stability of the disease-free equilibrium point and the local disease equilibrium point through the calculation of the basic regeneration number By introducing the concept of disease persistence, this paper explains the contagion process of stock market crisis when the basic regeneration number is greater than or equal to 1, and verifies that when the basic regeneration number, the stock market crisis can be completely eliminated. Next, we use matlab to simulate the spread process of the stock market risk, so as to test the reliability of this study. In the end, this paper combines and analyzes the existing research and the research of this paper, aiming at how to control and reduce the basic regeneration number to put forward appropriate crisis relief strategies for managers and relevant departments.

Keywords: SEIR model, risk transmission mechanism of stock market, disease-free equilibrium point, local stability

目录

摘要： I

Abstract II

第一章 引言 1

1.1 研究目的及意义 1

1.2 研究相关背景 2

1.2.1 国外相关研究回顾 2

1.2.2 国内相关研究回顾 3

1.3 本文的研究方法及创新点 4

第二章 理论模型概述、变量定义及稳定性分析 5

2.1 理论模型概述 5

2.1.1 SEIR模型建立 5

2.2基本再生数 6

2.3 无病平衡点的稳定性分析 7

第三章 疾病持续生存和动态均衡点 9

3.1 疾病持续生存 9

3.2地方病平衡点的局部稳定性分析 9

第四章 仿真模拟 12

4.1 模型随T变化规律 12

第五章 结论与建议 14

参考文献 16

致谢 18

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