随机因素及信息时间延迟对金融系统的影响

发布时间：2018-01-14 07:44

本文关键词：随机因素及信息时间延迟对金融系统的影响　出处：《云南大学》2014年博士论文　论文类型：学位论文

【摘要】：本文利用统计物理方法研究了随机因素及信息时间延迟对金融系统的作用。首先,对统计物理方法研究金融系统的现状、意义以及相关理论进行了全面的综述。其次,系统深入地研究了随机因素及信息时间延迟对金融系统的影响。基于Heston模型和单稳势函数分别刻画股票价格动力学动为,主要分析讨论了金融危机、随机共振和投资组合等情况的股票价格的统计特征。取得以下研究成果：第一部分工作分别研究了金融危机中的信息延迟对股票价格稳定性影响、投资风险收益和外部周期信息对金融市场稳定性的作用。首先,把时间延迟项引入到Heston模型,建立了时间延迟的股票价格动力学模型,利用随机模拟方法计算了描述股票价格运动的布朗粒子的平均逃逸时间,分析了信息延迟对股票价格稳定性的作用。结果表明,就强的(或弱的)股票价格需求弹性而言,存在一个最佳的(或最坏的)延迟时间对应着最强的(或最弱的)股票价格稳定性；在小的(或大的)延迟时间情况下,延迟时间和噪声源的关联强度对价格稳定性分别表现出相反的(或相同的)作用。其次,我们分析了延迟时间和初始位置刻画的投资时间和买入价格对股票投资的风险和收益的影响。结果显示,在强(或弱)股票价格需求弹性情况下,存在某一个延迟时间对应着最小的(或最大的)投资风险和最强的(或最弱的)平均股票价格收益及其稳定性；股票买入价格趋近亚稳态位置对应着较小的投资风险和较强的平均股票价格收益及其稳定性。最后,我们引入了乘性周期信息到Heston模型,建立了乘性周期信息驱动的股票价格崩盘模型,通过模拟计算平均逃逸时间,分析了外部周期信息对股票价格稳定性的作用。结果表明,外部周期信息强度的变化诱导平均逃逸时间关于波动平均恢复速度或初始买入价格的函数出现一个最大值：在平均逃逸时间关于波动的长期方差或者波动的振幅的函数中,观察到外部周期强度或频率的变化诱导的临界现象。第二部分研究工作,把外部和内部周期信息引入Heston模型,建立了周期信作用下股票价格动力学模型,研究了周期信息驱动的金融系统的随机共振现象和信息的时间延迟对共振现象的影响。通过模拟计算信号功率增益,观察到信号功率增益关于系统或外部驱动参量的函数中呈现一个逆共振现象,特别是在信号功率增益作为波动涨落振幅的函数中呈现双重逆共振现象。就时间延迟对共振现象作用而言,随着延迟时间的变化,在信号功率增益作为波动长期方差或噪声源关联强度的函数中,观察到了时间延迟诱导的临界现象。在第三部分的研究工作里,我们建立了投资组合模型,分析了投资组合分散度和投资周期对风险和收益的影响。结果显示,最大的投资组合分散度对应着最小的投资风险和最强的投资收益稳定性,而一个最坏的投资周期和投资周期的增大分别对应着最大的投资风险和变弱的投资收益稳定性。此外,这些模型得到的股票价格收益的概率密度函数、波动的概率密度函数、收益的关联函数和收益的逃逸时间的概率密度函数等统计特征与文献或者实际的金融数据的结果做了比较,发现模型和实际金融市场的结果是吻合的。
[Abstract]:In this paper, using the method of statistical physics to study random factors and time delay information to the financial system. Firstly, the status of the method of statistical physics, financial system research, significance and related theories comprehensively. Secondly, systematically study the random factors and the influence of time delay on the financial information system of the Heston model and the single. The steady potential function respectively describe the stock price dynamics is based on dynamic, mainly discusses the financial crisis, the statistical characteristics of stochastic resonance and portfolio of the stock price. The research results are as follows:
The first part of the work were studied in the financial crisis information delay influence on stock price stability, the role of investment risk return and external periodic information on the stability of the financial market. Firstly, the time delay is introduced into the Heston model, established the dynamic model of stock price time delay, the average escape time Brown particles to describe the movement of stock price calculation the use of stochastic simulation method, analyzed the effect of information delay on stock price stability. The results show that the strong (or weak) stock price elasticity of demand, there is a best (or worst) delay time corresponds to the strongest (or weakest) stock price stability in the small; the (or large) delay time, delay time and the strength of the correlation between noise sources on price stability respectively showed the opposite (or the same). Secondly, we analyze the Influence of delay of risk and return of stock investment time and the initial position characterizations of the investment of time and the purchase price. The results showed that in the strong (or weak) stock price demand elasticity, there is a delay time corresponding to the minimum (or maximum) and investment risk (strongest or weakest) average the stock price return and its stability; buy the stock price approaching the metastable position corresponds to smaller investment risk and higher average stock returns and stability. Finally, we introduce a multiplicative periodic information to the Heston model was established by periodic information driven stock price collapse model, through the simulation analysis of the mean escape time. The effect of external periodic information on stock price stability. The results show that the change of external periodic information intensity induced by the average escape time on average recovery rate or initial fluctuations The function of the initial buying price has a maximum value: in the function of the average escape time, the fluctuation of the long-term variance or the amplitude of the fluctuation, the critical phenomenon induced by the change of the external cycle intensity or frequency is observed.
The second part of the work, the introduction of Heston model of external and internal cycle information, set up the stock price dynamics model under the action of periodic signal, delay the financial system of periodic information driven stochastic resonance and information time impact on resonance phenomenon. Through the simulation of signal power gain, the observed signal power gain on a an inverse resonance function system or external driving parameters, especially the function in signal power gain as the fluctuations of amplitude in double inverse resonance phenomenon. The time delay effect on resonance phenomenon, with the change of delay time in signal power gain as a function of long-term fluctuation variance or noise source correlation strength in to observe the critical phenomena induced by time delay.
In the third part of the research work, we established a model of portfolio investment, portfolio investment cycle and effect of dispersion of the risks and benefits of the analysis. The results show that the stability of investment portfolio dispersion corresponds to the minimum investment risk and the strongest, and the increase of one of the worst investment and investment cycle cycle corresponding to the largest investment risk and weaker investment income stability.
In addition, the probability density function of these model stock price gains, the probability density function of the fluctuation, the correlation function and the income of the escape time of the probability density function of the statistical characteristics and the literature or the actual financial data results, found the model and actual financial market results are consistent.

【学位授予单位】：云南大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F224;F830.9

【共引文献】