带有延迟的金融类系统的稳定性与控制

发布时间：2018-06-23 00:58

本文选题：资产价格系统 + 延迟　；参考：《江南大学》2014年硕士论文

【摘要】：随着我国经济的发展，我国的金融市场也将会有更大的发展与突破。面对着诸多机遇和挑战，我国金融市场急需科学的理论作指导。通过对金融市场上诸多现象的观察，本文先后讨论了二维的带有延迟的资产价格系统的脉冲控制，三维的带有多延迟的股票价格系统的脉冲控制，构建了五维的多延迟的资产价格-利润模型，从不同的角度探讨了金融市场资产价格的复杂现象。研究表明脉冲控制的二维的带有延迟的资产价格系统，三维的带有多延迟的股票价格系统，五维的多延迟的资产价格-利润模型在探究问题的不同方法上表现出了各自的优越性。本文的研究主要包括以下几个方面：（1）给出原有的资产价格系统，通过对脉冲控制稳定性的进一步探讨，讨论了一个二维的带有延迟的连续资产价格系统的脉冲控制。首先，针对交易者的参量及时滞，分析了脉冲控制的资产价格系统所具有的特征。其次，通过构建Lyapunov函数，给出了脉冲系统的全局指数稳定的保守条件。对二维脉冲系统进行数值模拟，并对模拟结果进行了数值分析。仿真结果与理论分析相一致，说明了脉冲控制的资产价格模型在金融市场上的应用价值。（2）考虑到在金融市场条件下，基本价格同市场需求紧密关系，并且基本价格会依赖于市场需求做出调整。在原有的资产价格系统的基础上，通过对脉冲控制稳定性的探讨，讨论了一个三维的带有多延迟的股票价格系统的脉冲控制。同样是先针对交易者的参量及时滞，，分析了脉冲控制的股票价格系统所具有的特征。其次，通过构建Lyapunov函数，给出了脉冲系统的全局指数稳定的保守条件。对三维脉冲系统进行数值模拟，并对模拟结果进行了数值分析。仿真结果与理论分析相一致，说明了脉冲控制的股票价格模型在金融市场价格稳定性的探求过程中有着重要的应用价值。（3）考虑到我国金融市场的复杂性，基于金融市场上存在着股票价格和利润，提出并研究了五维的多延迟的金融市场价格-利润连续动力系统模型，该模型优化了离散的异结构模型,同时考虑了波动的基本面价格下的基础交易者和趋势跟随者根据利润的自适应转化行为，文章分析了延迟的线性近似微分系统的特征方程，进行了参数分岔分析，给出系统出现分岔行为及局部稳定的条件。理论结果显示不仅基础交易者和趋势跟随者的不同行为，而且波动的基本面价格都会对市场不稳定性产生影响。对含多延迟的复杂价格—利润系统进行数值模拟，并对模拟结果进行了数值分析。仿真结果进一步说明了带延迟的价格—利润模型所具有的特征，从而也证实了这种模型在描绘金融市场价格稳定性动态上的实用价值。
[Abstract]:With the development of our economy, our financial market will also have greater development and breakthrough. Faced with many opportunities and challenges, China's financial market urgently needs scientific theoretical guidance. Through the observation of many phenomena in the financial market, this paper has discussed the pulse control of the asset price system with delay in two dimensions and the pulse control of the stock price system with multiple delays in three dimensions. A five dimensional multi-delay asset price-profit model is constructed and the complex phenomena of asset price in financial market are discussed from different angles. The results show that the impulse-controlled two-dimension asset price system with delay, the three-dimensional stock price system with multi-delay, The five-dimensional multi-delay asset price-profit model shows its own advantages in different methods of exploring the problem. The research in this paper mainly includes the following aspects: (1) the original asset price system is given, and the stability of pulse control is further discussed. The pulse control of a two-dimensional continuous asset price system with delay is discussed. Firstly, the characteristics of the impulsive control asset price system are analyzed according to the traders' parameters and time delay. Secondly, the conservative condition of global exponential stability of impulsive systems is given by constructing Lyapunov function. The two-dimensional pulse system is numerically simulated and the simulation results are analyzed. The simulation results are consistent with the theoretical analysis, and the application value of the impulse control asset price model in the financial market is explained. (2) considering the close relationship between the basic price and the market demand under the financial market conditions, And basic prices will depend on market demand to make adjustments. On the basis of the original asset price system, the impulsive control of a three dimensional stock price system with multiple delays is discussed by discussing the stability of impulse control. At the same time, the characteristics of the stock price system based on impulsive control are analyzed in terms of the traders' parameters and delays. Secondly, the conservative condition of global exponential stability of impulsive systems is given by constructing Lyapunov function. The three-dimensional pulse system is numerically simulated and the simulation results are analyzed. The simulation results are consistent with the theoretical analysis, which shows that the impulse control stock price model has important application value in the process of exploring the price stability of the financial market. (3) considering the complexity of the financial market in China, Based on the existence of stock price and profit in the financial market, this paper proposes and studies a five-dimensional multi-delay model of price-profit continuous dynamic system in financial market. The model optimizes the discrete dissimilar structure model. At the same time, considering the basic trader and trend follower under the fluctuating fundamental price, according to the adaptive transformation behavior of profit, the characteristic equation of the delay linear approximate differential system is analyzed, and the parameter bifurcation analysis is carried out. The conditions for bifurcation behavior and local stability of the system are given. The theoretical results show that not only the behavior of the basic trader and the trend follower is different, but also the fluctuation of the fundamental price will affect the market instability. The complex price-profit system with multiple delays is numerically simulated, and the simulation results are analyzed. The simulation results further illustrate the characteristics of the price-profit model with delay, which also proves the practical value of the model in describing the price stability dynamics of financial markets.
【学位授予单位】：江南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.5;F224

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