本文選題：連續(xù)滲流　切入點(diǎn)：價格過程　出處：《北京交通大學(xué)》2012年博士論文　論文類型：學(xué)位論文

【摘要】：本論文運(yùn)用連續(xù)滲流、隨機(jī)交互作用系統(tǒng)、伊辛模型、選舉模型和Zipf定理等方法研究了證券市場中價格過程波動的統(tǒng)計特性,不同證券指數(shù)之間波動連鎖反應(yīng)的統(tǒng)計特性,上證和深證的寬尾現(xiàn)象和冪律分布.討論了價格過程模型下的歐式未定權(quán)益的定價和套期保值問題.研究了二維W-R模型的雙層隨機(jī)相分離線的統(tǒng)計特性.本論文的組織結(jié)構(gòu)如下. 第1章簡單介紹了金融數(shù)學(xué),特別是證券價格波動理論研究的發(fā)展背景、研究現(xiàn)狀.列出了本論文的主要研究成果. 第2章通過連續(xù)滲流理論研究證券價格過程波動的統(tǒng)計特性.連續(xù)滲流方法被應(yīng)用于建立金融模型,用以描述證券價格的行為,特別是描述金融市場里投資者的“羊群效應(yīng)”.運(yùn)用統(tǒng)計分析的隨機(jī)方法,我們證明了價格過程的特征函數(shù)收斂于Black-Scholes模型相應(yīng)的特征函數(shù). 第3章考慮證券價格之間連鎖反應(yīng)的統(tǒng)計特性.應(yīng)用交互作用系統(tǒng)和統(tǒng)計物理理論描述和研究證券市場的兩種證券指數(shù)的波動,研究了二者之間的交互反應(yīng)特性.本章中我們運(yùn)用隨機(jī)分析和雙隨機(jī)路徑模型研究了證券指數(shù)之間連鎖反應(yīng)的概率分布,進(jìn)一步,揭示出兩種證券指數(shù)模型波動的概率測度的漸近性,通過連鎖反應(yīng)的單只證券指數(shù)的概率性質(zhì).對所建立的金融模型的有限維概率分布收斂性進(jìn)行了討論. 第4章運(yùn)用隨機(jī)過程理論及隨機(jī)選舉模型理論,我們建立了一個包含兩種投資者類型的金融證券價格模型.我們運(yùn)用該金融模型來描述證券市場的單只證券價格過程性質(zhì)與波動.在該金融模型里,除了專業(yè)投資者,我們也考慮普通投資者或者說非專業(yè)投資者,這里停時理論和選舉模型被用來建立數(shù)學(xué)模型以及研究非專業(yè)投資者投資的統(tǒng)計特性.討論了該價格過程模型下的歐式未定權(quán)益的定價和套期保值問題. 第5章研究了二維Widom-Rowlinson模型的雙層隨機(jī)相分離線的統(tǒng)計特性.分離線把格點(diǎn)W-R模型的兩個共存相分隔開來,當(dāng)該模型的化學(xué)勢μ足夠大時,對描述相分離線波動的概率分布收斂性進(jìn)行了研究.模型引入backbone的概念,分析并發(fā)展了與polymer權(quán)重對應(yīng)的polymer-鏈及串展開方法.給出了二維W-R模型雙層隨機(jī)分離線的自由能的存在性. 第6章運(yùn)用Zipf-圖方法研究股票價格和交易量的波動特性,Zipf-圖方法已被廣泛地應(yīng)用于物理科學(xué)領(lǐng)域.在本章的第一部分,分析了來自于上證綜指和深證成指的股票價格和交易量數(shù)據(jù),并研究了它們的統(tǒng)計特性.我們選取了中國股市2002-2006年度每天的數(shù)據(jù),通過分析這些數(shù)據(jù),我們討論了寬尾現(xiàn)象的統(tǒng)計特性以及每天股票價格和交易量的冪律分布.在本章的第二部分,我們運(yùn)用Zipf-圖方法研究了2001-2006年期間上證和深證的寬尾現(xiàn)象和冪律分布. 第7章列出了一些與本研究密切相關(guān)的待解決的問題.這也是本人今后科研工作的目標(biāo)之一.
[Abstract]:This paper uses continuous seepage, random interaction system, Ising model, election model and the Zipf theorem and other methods to study the statistical characteristics of the price volatility in the stock market, the stock index fluctuation between different statistical characteristics of chain reaction, Shanghai and Shenzhen wide tail phenomenon and the power-law distribution. The price of European contingent claim process model the pricing and hedging problem. To study the statistical properties of the two-dimensional W-R model of double random phase separation line. This thesis is organized as follows.
The first chapter briefly introduces the development background of the research on financial mathematics, especially the theory of stock price fluctuation, and lists the main research results of this paper.
The second chapter through the statistical characteristics of the continuous flow theory of stock price volatility. The continuous flow process method is applied to establish a financial model, used to describe the stock price behavior, especially in the financial market investors "herd behavior". By using the stochastic method of statistical analysis, we prove that the characteristic function of the price process in convergence the characteristic function of the Black-Scholes model.
The third chapter consider the statistical characteristics of stock price between the chain reaction. The two stock index system and application of interaction of statistical physics to describe and study the stock market volatility on the interaction characteristics between the two probability distribution. In this chapter, we use stochastic analysis and double random path model to study the stock index between the chain reaction further, to reveal the asymptotic probability measure two stock index volatility model, the probabilistic properties of the single chain reaction of stock index. The financial model established by finite dimensional probability distribution of convergence is discussed.
The fourth chapter uses the theory of stochastic process and stochastic election model theory, we established a model of financial securities price includes two types of investors. We use this model to describe the financial securities market of individual securities price fluctuation. In the process of property and financial model, in addition to professional investors, we also consider ordinary investors or non professional investors, here the stopping time theory and the election model is used to establish the mathematical model and the study of non professional investors. Discuss the statistical characteristics of pricing and hedging of European contingent claims the price process model.
The fifth chapter studies the statistical properties of the two-dimensional Widom-Rowlinson model of double random phase separation line offline. The two coexist in the lattice W-R model is separated, when the chemical potential of the model is large enough, the probability distribution of convergence to describe the phase fluctuation offline was studied. The concept of backbone model is introduced. Analysis and development of the corresponding polymer weight polymer- chain and series expansion method. The existence of the 2D W-R model of double randompaths free energy.
The sixth chapter uses the fluctuation characteristics of stock price and trading volume of Zipf- diagram, Zipf- diagram method has been widely used in the physical sciences. In the first part of this chapter, the analysis from the Shanghai and Shenzhen stock stock price and trading volume data, and its statistical properties are studied. We selected the stock market Chinese 2002-2006 annual daily data, through the analysis of these data, we discuss the statistical characteristics of the wide tail phenomenon and power-law day stock price and trading volume distribution. In the second part of this chapter, we use the Zipf- method to study for 2001-2006 years during the Shanghai and Shenzhen wide tail phenomenon and the power-law distribution.
The seventh chapter lists some problems to be solved closely related to this study. This is also one of the goals of my future research work.

【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2012
【分類號】：F224;F832.51

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本文編號：1562464