金融复杂系统极端事件的非线性动力学研究

发布时间：2018-04-17 20:07

本文选题：复杂性科学 + 非线性理论　；参考：《中国海洋大学》2013年硕士论文

【摘要】：金融市场的高度快速发展是当代经济社会的重要特征之一，然而其在保持着高度活力的同时也会为我们带来潜在的巨大风险损失。所以研究金融系统的运行规律，了解金融极端事件的产生及再生传导机制，是当前金融研究领域的重要课题之一。金融市场是一个非常复杂的动力学系统，，它通过持续产生了一种规模宏大的高频数据序列来记录市场中众多参与者们（个体）共同决策的结果，且这些记录比较完整而且可以持续记录。也就是说，金融市场其实是一个真实的持续演变的复杂系统。而且这个复杂系统呈现了某种突现性质，即复杂系统的性质并不能仅仅是由各组成部分的性质轻松加和推断出来，必须仔细考虑个微观个体之间的相互影响与相互适应。本文按照复杂性科学的思想，紧密结合非线性系统动力学，通过深入研究金融时间序列的非线性特征，来考察我国金融系统大波动极端事件的相关运行规律。首先，我们对以证券市场为例的时间序列进行分析，探讨其是否来自独立同分布的随机过程。如果该数据来自非线性系统的结论得以确认，我们就可以进一步通过非线性定量分析的方法计算金融时间序列的有关非线性特征值。通过这些特征值，我们可以判断金融系统是否为混沌系统，并通过这些特征值对金融系统加以描述。如果金融系统确实具有混沌行为，那么我们可以探讨研究其金融时间序列是否具有长程相关性，金融系统的极端事件是否具有长程时间关联。如果存在长程记忆性我们就可以用重现时间间隔的相关方法对极端事件序列进行研究，以此揭示金融复杂市场极端事件的分布特征。最后，我们就可以在方法应用方面做一些探讨，为金融风险管理研究的开展提供相关建议。论文共分五个部分：第一部分为基础理论研究，该部分包含了复杂性科学理论、金融复杂系统理论以及金融时间序列的分析理论，详细介绍了金融复杂系统应该具有的理论特征和非线性学科中的混沌理论，为后续开展金融复杂系统极端事件的非线性动力学研究奠定理论基础。第二部分为金融复杂系统时间序列的确定性和非线性研究，该部分解决了对金融复杂金融系统下的极端事件进行时间序列的非线性动力学研究之前首先要弄清楚的两个问题，即动力系统的确定性和非线性检验，并对检验方法经行了创新，即为后文研究做好铺垫，也创新金融时间序列的研究方法。第三部分为金融复杂系统极端事件的长程时间关联研究，该部分用统计学中小概率事件的概念对金融系统的极端事件进行了统计界定，依据大气物理学中对极端事件的研究过程探索了金融复杂系统中极端事件序列具有的长程时间关联特征，对极端事件的预测与评估产生了重要影响。第四部分为金融复杂系统极端事件的再现时间间隔研究，该部分在金融复杂系统具有长程时间关联的基础之上，根据长期记忆性，运用金融物理学中的再现时间间隔方法推理极端事件的再现时间间隔分布，构造以收益率为例的风险评估模型，丰富金融系统极端事件的研究方法。第五部分是全文最后一章，即全文总结与未来展望部分。这部分内容主要是对论文的研究意义、研究内容、研究结论做一个概括性的总结；给出论文在下一步需要改进的地方，需要做出的完善，并写了几点相关建议供市场监管者参考。
[Abstract]:The rapid development of financial markets is one of the most important characteristics of modern society . However , it also brings great risk losses to us while maintaining high vitality . Therefore , it is one of the important topics in the field of financial research .

Financial markets are a very complex dynamic system by which a large scale of high - frequency data sequences are continuously generated to document the results of a large number of participants ( individuals ) in the market , and these records are relatively complete and sustainable . That is , financial markets are actually a real and evolving complex system . And this complex system presents some kind of unexpected nature , that is , the nature of the complex system cannot be easily added and inferred from the nature of the components , and the interaction and adaptation between individual micro - individuals must be carefully considered .

Based on the thought of complexity science and closely combined with the nonlinear system dynamics , we study the nonlinear characteristics of the financial time series by studying the nonlinear characteristics of the financial time series . First , we can find out whether the financial system is a chaotic system or not . If the data comes from the nonlinear system , we can further study whether the financial system is a chaotic system or not . If there is long - range memory , we can find out whether the financial system is a chaotic system or not .

The first part is divided into the basic theory research , this part contains the theory of complexity science , the theory of financial complex system and the analysis theory of financial time series , details the theory characteristic of financial complex system and the chaos theory in nonlinear subject , and lays a theoretical foundation for the follow - up of nonlinear dynamic study of extreme events of financial complex system .

The second part is the deterministic and non - linear research on the time series of financial complex system , which solves two problems before the nonlinear dynamic study of the time series of extreme events in the financial complex financial system .

The third part is the long - range time correlation study of the extreme events of the financial complex system , which defines the extreme events of the financial system by means of the concept of the statistical small probability event . According to the research process of the extreme events in the atmosphere physics , the long - range time correlation characteristics of the extreme event sequences in the financial complex system are explored , and the prediction and evaluation of the extreme events have an important influence .

The fourth part is divided into the research on the reproduction time interval of the extreme events of the financial complex system . The part is based on the long - range time correlation of the financial complex system . According to the long - term memory , the reproduction time interval distribution of the extreme events is inferred based on the reproduction time interval method in the financial physics , and the risk evaluation model taking the yield as an example is constructed , and the research method of the extreme events of the financial system is enriched .

The fifth part is the last chapter of the whole text , that is , the whole - text summary and the future prospect . This part is mainly about the research significance , the research content and the research conclusion of the thesis .
In the next step , the paper gives the improvement of the paper , needs to be perfected , and writes several relevant suggestions for reference to market regulators .

【学位授予单位】：中国海洋大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

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