论文标题:金融市场收益率离散数学模型及其定性分析
The Qualitative Analysis of Discrete Mathematical Models on the Rate of Return in Financial Market
论文作者
论文导师 庾建设,论文学位 博士,论文专业 应用数学
论文单位 湖南大学,点击次数 827,论文页数 88页File Size2601K
2006-03-15论文网 http://www.lw23.com/lunwen_333587/
The financial market; the rate of return; Amount of circulating fund; difference equation; stability; the periodic oscillation
本文主要应用差分方程的基本理论(包括时滞差分方程理论与脉冲差分方程理论)与基本方法研究了金融市场收益率的稳定性及其变化规律。针对各种不同的金融背景，建立了一系列金融网络中揭示收益率稳定性及其变化规律的差分方程模型。应用现代差分方程理论对这些数学模型解的渐近性态与周期振荡进行了详细的讨论研究。这些研究结果在一定程度上阐明了金融领域收益率变化的若干内在规律，并对金融市场的稳定性做出了解释和预测，对金融理论的研究和发展有重要的意义，也可为金融领域宏观决策提供一种新的依据，具有重要的应用价值。 第二章主要是在各种不同的金融背景下，建立了一系列相应的离散收益率-流通量模型。具体说来，在相对封闭的金融网络中，我们建立了反映金融网络中各节点即时收益率变化的基本方程。考虑到任何一个金融网络都具有开放性，我们对开放的金融网络建立了相应的数学模型。由于从投资到获利需要一定的时间，针对这种现象，我们对收益率-流通量方程进行了改进，建立了离散的具有时滞的收益率-流通量方程。前面给出的三个方程都是在常规情形下建立的，但是，许多突发现象能够引起市场的波动，为此我们又建立了有突发事件发生时的收益率—流通量方程。 第三章至第六章，我们对第二章建立的各类方程分别进行详细的讨论。应用现代差分方程定性理论与稳定性理论等知识，研究了这些方程平衡解的稳定性，周期解与边值问题解的存在性以及多解性等问题。本文第三章证明了各结点收益率加权和为常数即金融市场收益率均衡原理，得到各结点收益率极限为整个网络平均收益率的条件；第四章研究了开放金融网络中离散的收益率—流通量方程模型，用差分方程稳定性理论得到模型平衡解稳定的条件；第五章主要研究具有时滞的金融网络收益率—流通量方程，并给出了具有时滞金融网络的收益率流通量方程平衡解稳定以及具有周期解的条件。本文第六章研究了出现突发事件时的收益率—流通量方程，证明了不同时间段的网络平均收益率也不相同，并且随脉冲条件的变化而变化，同时给出了相邻两个时间段网络平均收益率之间的关系。 以上这些研究结果分别对应各种不同背景下金融网络收益率变化的客观规律，从而对若干金融现象作出了有价值的解释和预测。
This thesis mainly concerns the stability of the rate of return in the financial market by applying the basic theories and methods of difference equations (including the theory of delay difference equations and the theory of impulsive difference equations). Corresponding to various different financial backgrounds, a series of difference equation models are built up to reveal the stability and laws of the rate of return in the financial network. The asymptotical behaviors and periodic oscillations have been studied by applying the modern theories of difference equations. These results clarify some essential regulations of the rate of return in the financial fields and can be used to estimate and predict the stability of the financial market. Also, these researches are of importance to the development and completeness of the financial theory and can provide a kind of new basis for the macro1 view decision in financial field.In Chapter 2, a series of discrete rate of return-amount of circulating fund models (discrete RRACF model) are built up under various different financial backgrounds. More specifically, concerning the relatively closed financial network, we build up a basic discrete RRACF model reflecting the law of instant rates of return of each node in the financial network. Since every financial network is open, we build up a model corresponding to the open financial network. Usually, getting the profit need some time after investing. So we improve the rate of return-amount of circulating fund equation and build up a new discrete equation with delay. All of the three equations are established in the case of the normal situation. However, many abrupt phenomena can cause the wave of a financial market. Duo to this, we build up another equation concerning the rate of returns and the amount of circulating fund with impulsive terms.Chapter 3- Chapter 6 mainly deals with the detailed discussion on the equations established in Chapter 2. By applying the modern qualitative theory and stability theory of difference equations, we study the stability of the equilibrium, the existence and multiplicity of periodic solutions and solutions of boundary value problems etc. In Chapter 3, we obtain the Equilibrium Principle of the Rate Return in Financial Market, that is, the weighted sum of instant rate of return of nodes in the network is a constant. For each node, its instant rate of return tends to the average rate of return of whole network; Chapter 4 deals with the discrete rate of
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