论文总字数：17499字

摘 要

在股票市场间的联动性越来越强的前景下，股票之间也越来越容易传染风险。本文将研究股票市场，以及具有双时滞的传染病模型，并将它们结合起来，根据SEIRS传染病模型分析股票市场之间的风险传染机制，并进行实证研究，分析了股票市场风险的宏观规律和法则。

首先运用Liapunov函数证明了本文所构建的传染模型的局部和全局渐近稳定性；然后研究基本再生数，得出结论：基本再生数决定了股票市场之间的风险传染，如果基本再生数比1大，那么其他子市场将会被其中一个子市场的股票市场风险传染，股票市场传染风险和这个值呈正比关系；最后引进贝叶斯人工神经网络算法，并结合正则化算法反演求出该传染模型的参数值，得出结论：有一种流行病平衡点()存在于我国股票市场对应的传染病模型里，同时一个局部的和全局的平衡点也存在于其中。时滞项的分析显示，调整第一时滞项的大小是可行的，因为传染模型平衡点的稳定性的影响因素很大取决于第一时滞项。政策调整以后，改变系统稳定点的属性，促进经济增长，参数反演的结果与上述仿真结果基本一致。这说明贝叶斯神经网络在参数算法中的应用是可行的。资金的有效传导率、资金转移率决定了股票市场风险扩散的趋势，并单独使用事前防御或事后预防的控制策略效率低下，使用这两种策略可以控制风险的传播。

为了有效防止股票市场风险在市场间的传播，我国应完善股票市场的基础设施，提高股票市场的直接免疫力；建立科学的股票市场风险监测预警机制，有效地实现提前防范股票市场风险；建立风险隔离机制，降低风险股票市场之间风险传递的概率，优化了股票市场监管体系，提高了股票市场风险防范的整体能力。

关键词：股市风险，双时滞的SEIRS模型，基本再生数，贝叶斯神经网络

Application of a class of SEIRS model with double time delay in stock market risk management

Abstract

In the prospect of increasing interaction between stock markets, stocks are more and more vulnerable to contagion risk. This paper combines the stock market with the infectious disease model with double time delay, analyzes the risk transmission mechanism between the stock markets on the basis of the SEIRS infectious disease model, and makes an empirical study, and analyzes the macro laws and rules of the stock market risk.

Firstly, by using Liapunov function，we have proved the local and global asymptotic stability of the contagion model constructed that is in this paper. Then we study the basic update number and find that the basic update number determines the risk transfer between stock markets, if the basic regeneration number is larger than 1, Then the other sub-markets will be infected by the stock market risk of one of the sub-markets, and the risk of stock market contagion will be proportional to this value. Finally, the Bayesian artificial neural network algorithm is introduced, and the parameter values of the contagion model are obtained by combining the regularization algorithm. It is concluded that there is an epidemic equilibrium point () existing in the infectious disease model corresponding to the stock market in China. At the same time, a local and global equilibrium also exists in it. The analysis of the time delay term shows that it is feasible to adjust the size of the first delay term, because the stability of the equilibrium point of the contagious model depends heavily on the first delay term. After the policy adjustment, change The properties of the stable point of the system are changed to promote economic growth. The parameter inversion results are consistent with the above simulation results basically. It shows that the application of bayesian neural network in parametric algorithm is feasible. The effective transmission rate and capital transfer rate of the fund determine the trend of risk diffusion in the stock market, and the use of pre-defense or post-prevention control strategies alone is inefficient. The use of these two strategies can control the spread of risk.

In order to effectively prevent the spread of stock market risk among markets, our country should perfect the infrastructure of stock market, improve the direct immunity of stock market, establish a scientific monitoring and early warning mechanism of stock market risk, and effectively and realistically. At present, the risk of stock market is prevented in advance, the mechanism of risk isolation is established, the supervision system of stock market is optimized, and the overall ability of risk prevention in stock market is improved.

Keywords: Stock Market Risk, SEIRS Model With Double Time Delay, Basic Regeneration Number, Bayesian Neural Network

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 国内外相关研究回顾 1

1.3 本文的研究方法及创新点 3

第二章 具有双时滞的SEIRS模型的建立 5

2.1 股票市场风险的定义和特征 5

2.2 经典的传染病模型 5

2.3 双时滞SEIRS模型的建立 5

2.4系统平衡点的稳定性 9

2.5基本再生数的分析 10

第三章 传染模型的参数确定 11

3.1 贝叶斯正则化神经网络 11

3.2 参数反演算法 11

3.3 参数反演的实证研究 12

第四章 结论与建议 17

参考文献 19

致谢 21

第一章 引言

1.1 研究目的及意义

在全球金融创新发展越来越成熟的情况下，金融结构中的系统性风险和传染风险也越来越大，所以我们对这类风险进行精准的度量是达到有效管理的一种手段。其中股票市场的个体抛售和股民无思绪的盲目“跟风”导致对股票市场风险与人类的传染病的传播机制相似，二者都会以个体为传染源波及整个群体，最终造成大规模的混乱。另一方面，个体投资者和上市公司采取的不同措施也直接影响到了股票市场。当出现个体将某股票抛出或收购，其他不知情的人也存在同样抛出或收购的跟风行为，可能会导致整个股票市场出现大萧条或者异常繁荣的景象。

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