本文選題：穩(wěn)定分布　切入點(diǎn)：PPS分布　出處：《蘭州理工大學(xué)》2013年碩士論文

【摘要】：資產(chǎn)收益率的分布假設(shè)是現(xiàn)代金融市場進(jìn)行風(fēng)險(xiǎn)分析的重要前提。傳統(tǒng)的投資組合都假設(shè)資產(chǎn)收益率服從正態(tài)分布,但是大量的實(shí)證研究表明并非如此,資產(chǎn)收益率不服從正態(tài)分布,往往具有“尖峰”和“厚尾”的特征,這是正態(tài)分布不能描述的。早期許多學(xué)者的研究都表明,股票及其它金融資產(chǎn)的收益率都表現(xiàn)為非正態(tài)分布的特征,如果用正態(tài)分布來描述收益率效果往往很差。后來Mandelbrot從收益率分布具有的“尖峰厚尾”特征出發(fā),用穩(wěn)定分布描述資產(chǎn)收益率。此后,穩(wěn)定分布在金融中得到了重視,許多學(xué)者進(jìn)行了廣泛的研究。研究表明,穩(wěn)定分布對資產(chǎn)收益率的擬合效果很好。本文從穩(wěn)定分布的基本性質(zhì)出發(fā),對穩(wěn)定分布在保險(xiǎn)理賠與多期投資組合中的應(yīng)用進(jìn)行研究。 介紹了一元穩(wěn)定分布的兩種定義；介紹了一元穩(wěn)定分布的主要性質(zhì)以及穩(wěn)定分布主要的參數(shù)估計(jì)方法。 從生成方法、分布函數(shù)、密度函數(shù)以及分位函數(shù)方面,介紹了穩(wěn)定分布的一種特殊情形—帕累托嚴(yán)格穩(wěn)定分布(PPS)；介紹了帕累托嚴(yán)格穩(wěn)定分布的三種參數(shù)估計(jì)方法；用保險(xiǎn)數(shù)據(jù)對帕累托嚴(yán)格穩(wěn)定分布在保險(xiǎn)中的應(yīng)用進(jìn)行實(shí)證研究,發(fā)現(xiàn)PPS分布可以很好的擬合保險(xiǎn)理賠中的數(shù)據(jù),并且比較帕累托嚴(yán)格穩(wěn)定分布與正態(tài)分布和指數(shù)分布,發(fā)現(xiàn)PPS分布更適合擬合保險(xiǎn)數(shù)據(jù)。 在基金分離理論下,從風(fēng)險(xiǎn)厭惡型投資者的視角,在非正態(tài)穩(wěn)定分布條件下研究多期投資組合模型。研究了非正態(tài)穩(wěn)定分布條件下市場上含有多個(gè)風(fēng)險(xiǎn)證券和一個(gè)無風(fēng)險(xiǎn)證券時(shí)的多期投資組合,建立了多期投資組合模型；加入新的假設(shè),對模型進(jìn)行改進(jìn),并對模型的求解及其應(yīng)用條件進(jìn)行分析；用美國股票收益率數(shù)據(jù)進(jìn)行實(shí)證研究,給出多支股票多期投資組合的最優(yōu)投資組合策略。
[Abstract]:The assumption of asset return distribution is an important prerequisite for risk analysis in modern financial markets. Traditional portfolios assume that the return on assets is normally distributed, but a large number of empirical studies show that this is not the case. The rate of return on assets is usually characterized by "peak" and "thick tail", which can not be described by normal distribution. The return rate of stocks and other financial assets is characterized by non-normal distribution, and it is often very bad to describe the return rate by normal distribution. Later, Mandelbrot starts from the "peak and thick tail" characteristic of yield distribution. Since then, stable distribution has been paid more attention to in finance, and many scholars have carried out extensive research. Based on the basic properties of the stable distribution, this paper studies the application of the stable distribution in insurance claims and multi-period portfolio. In this paper, two definitions of univariate stable distribution are introduced, and the main properties of univariate stable distribution and the main parameter estimation methods of the stable distribution are introduced. In this paper, a special case of Pareto strictly stable distribution is introduced in terms of generating method, distribution function, density function and quantile function, and three parameter estimation methods of Pareto strictly stable distribution are introduced. The application of Pareto strictly stable distribution in insurance is studied by using insurance data. It is found that PPS distribution can fit the data of insurance claims very well, and compare Pareto strictly stable distribution with normal distribution and exponential distribution. It is found that PPS distribution is more suitable for fitting insurance data. Under the theory of fund separation, from the perspective of risk-averse investors, The multi-period portfolio model is studied under the condition of non-normal stable distribution. The multi-period portfolio with multiple risk securities and one risk-free portfolio is studied under the condition of non-normal stable distribution, and the multi-period portfolio model is established. By adding new assumptions, the model is improved, and the solution of the model and its application conditions are analyzed, and the optimal portfolio strategy of multi-stock multi-period portfolio is given by using the American stock return data.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：O211.3;F830.59

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