基于复杂系统理论的金融市场动力学研究

发布时间：2018-01-18 05:33

本文关键词：基于复杂系统理论的金融市场动力学研究　出处：《中国科学技术大学》2013年博士论文　论文类型：学位论文

【摘要】：随着世界经济贸易的日益频繁,金融市场正发挥着越来越重要的作用,对金融市场的研究也引起了各领域的关注。另一方面,复杂系统理论研究了当相互之间存在复杂非线性相互作用的个体自组织形成一个整体时所涌现出的宏观规律,特别地,当个体具有智能体的特性时,该复杂系统将呈现各种有趣的性质,这样的系统有金融市场、生物学系统等。利用复杂系统理论、统计物理、应用数学、非线性科学以及理论物理等手段来研究金融市场中的物理规律正发展成为一门新兴研究热点,被称为金融物理学。本研究采用复杂系统以及统计物理等理论,根据研究方法从以下三个方面研究了金融市场的动力学演化特性： 1.采用湍流理论中的SL层次结构模型研究股票价格序列的层次结构和多重分形特性。 SL层次结构理论最初用于解释湍流中发现的非线性标度律,其优点在于仅用间歇参数β、最奇异标度指数h0、余维数C三个参数就能够较好地描述和解释多重分形非线性标度行为。由于湍流和金融时间序列的描述存在相似之处,我们用SL层次结构理论对股票价格序列进行分析后发现,金融时间序列不仅具有多重分形性,而且存在SL层次结构。用三个参数分别对发达和新兴的金融市场中的非线性标度行为进行量化后比较得出,证券市场的多重分形程度与经济发展水平和地理位置等因素有关,且层次结构会随着市场的演化而变化。本文的研究成果能够帮助我们更好地理解金融市场的多重分形性质,且可以利用湍流中与SL层次结构相关联的多变量级联过程来解释金融市场中的动态演化。 2.将金融市场看作一个由多个交易者和投资产品所组成的复杂网络,利用复杂网络的理论对证券市场的资产回报序列进行建模,研究网络的静态拓扑结构和动态演化。采用阈值和滑动窗技术,我们分别构造了基于动态阈值和静态阈值的动态全局金融网络,并进一步计算了网络的三个全局特征参数平均度、最短路径长度和平均聚类系数分别随时间演化的曲线,从而研究网络拓扑结构的动态变化规律及其与历史上所发生的金融事件之间的联系。我们发现,三个参数都在金融风暴发生期间出现了异常的波动。该研究结果表明,金融危机与证券市场价格走势的统计性质之间存在着因果关系,因而研究动态的金融网络有助于我们更深入地理解经济危机的发生和传播机制。 3.构建一个包含投资者和投资产品的人工金融市场,考察市场的动态演化过程。我们提出的市场生态学模型不仅考虑投资者的动力学演化,而且考虑投资产品的动力学行为,在该模型中,投资者根据投资策略的不同分为两种类型：主动投资者掌握较多的市场信息,投资策略更为优化,因而选择优良资产的能力较强；被动投资者由于只能获取少量信息因而投资能力弱于主动投资者。这与实际市场的情况相符合,因为现实中每个投资者都只能掌握市场的部分信息。另一方面,投资产品根据它们的品质可以分为优良资产和劣质资产,优良资产的品质高于劣质资产,更能吸引投资者进行投资,但是优质产品的成本要高于劣质产品。模拟结果发现,在没有任何外界调控的情况下,系统依靠投资者的投资策略和与投资产品的相互作用,运行到足够长时间能够自组织地到达一个准静态,在准静态系统的交易者和投资产品的数量都维持着一个动态的平衡,且不同的影响因素能够带来不同的准静态性质,这与生态系统有着类似的性质,对实际金融市场的动态演化和金融危机的发生和恢复有一定的指导意义。
[Abstract]:With the world economy and trade have become increasingly frequent, financial markets are playing an increasingly important role in the study of financial market has also attracted attention in various fields. On the other hand, the theory of complex system is studied when there are complex nonlinear interactions between individual self organization form a macroscopic law, whole emergence each other in particular, when the individual has agent, the complex system will present a variety of interesting properties, such a system of financial markets, biological systems. The use of complex system theory, statistical physics, applied mathematics and theoretical physics, nonlinear science and other means to study the laws of physics in the financial market is becoming a new research hotspot, known as econophysics.
In this study, the dynamic evolution characteristics of the financial market are studied from the following three aspects: complex systems and statistical physics.
1. the hierarchical structure and multifractal characteristics of the stock price sequence are studied by the SL hierarchy model in the turbulence theory.
The SL hierarchy theory originally used to explain the nonlinear turbulence found in the scaling law, the utility model has the advantages of using only intermittent parameter, the singularity exponent H0, codimension three C parameters can be used to describe and explain the nonlinear multifractal scaling behavior. Due to turbulence and financial time series describing the similarities SL, we use hierarchical structure theory of stock price series analysis found that financial time series not only has the multifractal, and SL hierarchy. By three parameters are nonlinear in developed and emerging markets in the scaling behavior was quantified after comparison, the multi fractal degree and economic development the level and geographic location and other factors of the stock market, and the structure will change with the market's evolution. The results of this research can help us better understand the financial market more heavy The fractal properties can be used to explain the dynamic evolution in the financial market by the multivariable cascade process associated with the SL hierarchy in turbulence.
2., we regard the financial market as a complex network composed of multiple traders and investment products. We use the complex network theory to model the asset return sequence in the stock market, and study the static topology and dynamic evolution of the network.
The threshold and sliding window technique, we constructed the dynamic global financial network dynamic and static threshold based on threshold, and further calculate the network characteristic parameters of the three global average degree, shortest path length and the average clustering coefficient respectively with time evolution curve between dynamic changes of network topology and what happened in the history of financial events. We found that the three parameters during the financial turmoil has abnormal fluctuations. The results show that there exists a causal relationship between the statistical properties of the financial crisis and the stock market price movements, so the research of dynamic financial network have occurred and communication mechanism to help us more understanding of the economic crisis.
3. build a contains investors and investment products, artificial financial market, the dynamic evolution of the market. The market ecology model we proposed not only consider the dynamics and evolution of investors, consider the dynamical behavior of investment products, in this model, investors according to different investment strategies into two types: active investors have more the market information and investment strategies to optimize, and excellent asset selection ability is strong; passive investors can only get a small amount of information and weak investment in active investors. This with the actual market situation is consistent, because part of the information of each investor can only grasp the reality of the market. On the other hand, according to their investment products the quality can be divided into good assets and bad assets, excellent asset quality than inferior assets, can attract more investors for investment The capital, but the quality of the product cost is higher than that of inferior products. The simulation results show that in the absence of any external control, interaction systems rely on the investment strategy for investors and investment products, enough to run long time can automatically reach a quasi static, had maintained a dynamic equilibrium in quantity quasi static system products traders and investment, and the influence of different factors can bring different quasi static properties, which have similar properties and ecological system, the actual financial market dynamic evolution and the occurrence of financial crisis and has certain guiding significance to recover.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F830.91;N941.4

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