發(fā)布時間：2018-05-18 07:32

  本文選題：金融物理 + 隨機Ising系統(tǒng)��； 參考：《北京交通大學》2014年博士論文

【摘要】：全球化及互聯(lián)網的發(fā)展使得金融市場的發(fā)展更加迅速,并滲入到人們日常生活工作的各個方面.從微觀結構了解金融市場的形成機制及特征,對理解金融市場波動和管理金融風險有著很重要的作用.金融系統(tǒng)的復雜特性源于市場參與者之間的相互作用,研究這些參與者的行為對了解復雜系統(tǒng)的特性非常重要.因此,本文利用統(tǒng)計物理中的Ising動力學系統(tǒng),建立投資者相互影響的金融市場模型來了解價格形成及影響機制,并定義了該模型對應的收益率時間序列.通過對所構建的金融模型進行計算機模擬,并對模擬的收益率序列進行統(tǒng)計分析,我們發(fā)現(xiàn)利用Ising系統(tǒng)建立的金融模型可以重現(xiàn)金融價格波動的重要特性,如尖峰厚尾性、收益率尾部的power-law特性、絕對收益率序列的長記憶性及收益率序列的多重分形等特性Ising動力學系統(tǒng)模型中個體參與者之間的相互作用給金融市場中動態(tài)變化和互惠關系給出了新的見解.這個跨學科建模的成功,意味著有自然界存在著的物理共同點并值得我們去探索.全文的組織結構如下： 第一章中,介紹研究的背景和意義及本文的研究內容和創(chuàng)新點. 第二章中,著重介紹Ising系統(tǒng)的起源和發(fā)展,二維Ising系統(tǒng)的定義及特性,最后說明如何將隨機Ising系統(tǒng)及其機制應用于構建金融市場價格模型. 第三章中,在二維隨機Ising自旋模型的基礎上建立金融市場的價格模型,將投資者每一天的受影響強度隨機化.在邊界分別為零邊界、弱邊界及強邊界的情況下,建立了相應的金融模型.不同的邊界代表著不同的投資環(huán)境.為了對比模擬的數據和實際金融市場的數據,我們分析了上證綜合指數,深證成分指數和滬深300指數對應的收益率序列的統(tǒng)計特性,如波動聚集性、厚尾現(xiàn)象,絕對收益率尾部的power-law分布和分形現(xiàn)象.當邊界全為正邊界,即τ6的時候,深度參數y比零邊界τ1和弱混合邊界τ2,τ3要小,并且τ6的尾部指數變化范圍比其它五種邊界條件要小. 第四章中,我們用隨機Ising模型研究金融收益率序列的波動性,并且把我們的研究結果和中國證券市場過去22年的實證結果進行比較,找出判別股市中大的和小的風險的臨界點.從模型的微觀角度,我們解釋了波動率是如何變化的,這可以給金融市場的風險管理提供一定的建議. 第五章中,我們在Sierpinski格點地毯上使用Ising自旋模型建立金融模型.分形現(xiàn)象在自然界中普遍存在,分形格點的引入打破了每個投資者所受影響來源都是四個鄰居的情況.為了研究此金融模型的波動特性,我們用Monte Carlo模擬和數值研究方法,以及統(tǒng)計分析和多重分形分析來研究金融時間序列.不同大小的Sierpinski格點地毯和Ising動態(tài)的受影響強度來得到不同的多重分形譜.我們還研究模擬價格序列、上證綜合指數、深證成分指數、道瓊斯工業(yè)平均指數、納斯達克綜合指數、SP500指數、恒生指數及日經225指數對應的收益率序列的統(tǒng)計特性,隨時間變化的波動聚類現(xiàn)象和多重分形特性等.研究表明Sierpinski格點地毯上的金融模型可再現(xiàn)經驗數據的重要特征. 第六章中,基于金融市場中投資者之間的相互作用及投資環(huán)境的影響,應用Ising動力學系統(tǒng)和平均場理論建立了符合股市特點的股市價格方程.借助于計算機軟件Matlab,用Monte Carlo模擬方法,通過調整金融模型中的參數得到收益率序列.分析發(fā)現(xiàn)Ising動力系統(tǒng)構造的收益率同證券市場股票指數波動率—樣具有尖峰厚尾等統(tǒng)計特征.對模擬收益率原序列及混洗后的序列進行多重分形分析,我們發(fā)現(xiàn)模擬收益率序列存在分布多重分形和相關性多重分形的結論. 第七章是對本論文的總結及工作的展望.
[Abstract]:The development of globalization and the Internet has made the development of the financial market more rapid and permeated all aspects of people's daily life. Understanding the formation mechanism and characteristics of the financial market from the micro structure is very important for understanding the volatility of the financial market and managing the financial risks. The complex characteristics of the financial system are derived from market participation. The interaction between the participants is very important to understand the characteristics of the complex systems. Therefore, this paper uses the Ising dynamic system in statistical physics to establish a financial market model with mutual influence by investors to understand the mechanism of price formation and influence, and to define the corresponding return time series of the model. On the basis of the computer simulation of the established financial model and the statistical analysis of the simulated return sequence, we find that the financial model established by the Ising system can reproduce the important characteristics of the volatility of the financial price, such as the peak thick tailing, the power-law characteristics of the return rate tail, the long memory and the order of return of the absolute return sequence. The interaction between individual participants in the Ising dynamic system model of multi fractal and other characteristics gives new insights into the dynamic and reciprocal relationships in the financial market. The success of this interdisciplinary modeling means that there are physical common points in nature and deserve our exploration. The structure of the full text is as follows:
In the first chapter, we introduce the background and significance of the study, as well as the research contents and innovations of this paper.
In the second chapter, we focus on the origin and development of the Ising system, the definition and characteristics of the two-dimensional Ising system, and finally explain how to apply the random Ising system and its mechanism to the construction of the price model of the financial market.
In the third chapter, the price model of the financial market is built on the basis of the two-dimensional random Ising spin model, and the investor's affected intensity is randomised every day. In the case of zero boundary, weak boundary and strong boundary, the corresponding financial model is established. The different boundary represents different investment environment. Data and real financial market data, we analyze the statistical properties of the Shanghai Composite Index, the deep evidence component index and the Shanghai and Shenzhen 300 index, such as volatility aggregation, thick tail phenomenon, the power-law distribution and fractal phenomenon at the tail of absolute return. When the boundary is all positive boundary, that is, Tau 6, the depth parameter is y to zero. The boundary tau 1 and the weak mixing boundary 2, tau 3 are small, and the tail index of tau 6 is smaller than the other five boundary conditions.
In the fourth chapter, we use the random Ising model to study the volatility of the financial return sequence, and compare our results with the empirical results of the Chinese stock market for the past 22 years to find out the critical point of identifying the large and small risks in the stock market. From the microscopic perspective of the model, we explain how the volatility is changing, which is possible. In order to provide some suggestions for risk management in financial market.
In the fifth chapter, we use the Ising spin model on the Sierpinski lattice carpet to establish a financial model. The fractal phenomenon is common in nature. The introduction of fractal lattice breaks the situation that each investor is affected by four neighbors. In order to study the volatility of the financial model, we use Monte Carlo to simulate and value the numerical value. Research methods, statistical analysis and multifractal analysis to study the financial time series. Different sizes of Sierpinski lattice carpet and the affected intensity of Ising dynamics are different multifractal spectra. We also study the simulated price series, the Shanghai Composite Index, the deep evidence component index, the Dow Jones industrial average index, the NASDAQ ensemble. The statistical properties of the index, the SP500 index, the Hang Seng Index and the 225 index of the Nikkei index, the fluctuation clustering and the multifractal characteristics with time change, show that the financial model on the Sierpinski lattice carpet can reproduce the important characteristics of the empirical data.
In the sixth chapter, based on the interaction between investors and the influence of the investment environment in the financial market, the stock market price equation is established by using the Ising dynamic system and the mean field theory. With the help of the computer software Matlab, the return sequence is obtained by adjusting the parameters in the financial model by using the Monte Carlo simulation method. The analysis found that the yield of the Ising power system and the stock index volatility - the stock index volatility has the statistical characteristics of peak and thick tail and so on. The multiple fractal analysis of the original sequence of simulated return and the sequence of mixed washing is carried out, and we find that there is a conclusion that there is a multi fractal distribution and a correlation multifractal in the simulated return sequence.
The seventh chapter is the summary of the thesis and the prospect of the work.
【學位授予單位】：北京交通大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：F830.91;F224

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本文編號：1904975