稳定分布在保险与多期投资组合中的应用

发布时间：2018-03-30 13:15

本文选题：稳定分布　切入点：PPS分布　出处：《兰州理工大学》2013年硕士论文

【摘要】：资产收益率的分布假设是现代金融市场进行风险分析的重要前提。传统的投资组合都假设资产收益率服从正态分布,但是大量的实证研究表明并非如此,资产收益率不服从正态分布,往往具有“尖峰”和“厚尾”的特征,这是正态分布不能描述的。早期许多学者的研究都表明,股票及其它金融资产的收益率都表现为非正态分布的特征,如果用正态分布来描述收益率效果往往很差。后来Mandelbrot从收益率分布具有的“尖峰厚尾”特征出发,用稳定分布描述资产收益率。此后,稳定分布在金融中得到了重视,许多学者进行了广泛的研究。研究表明,稳定分布对资产收益率的拟合效果很好。本文从稳定分布的基本性质出发,对稳定分布在保险理赔与多期投资组合中的应用进行研究。介绍了一元稳定分布的两种定义；介绍了一元稳定分布的主要性质以及稳定分布主要的参数估计方法。从生成方法、分布函数、密度函数以及分位函数方面,介绍了稳定分布的一种特殊情形—帕累托严格稳定分布(PPS)；介绍了帕累托严格稳定分布的三种参数估计方法；用保险数据对帕累托严格稳定分布在保险中的应用进行实证研究,发现PPS分布可以很好的拟合保险理赔中的数据,并且比较帕累托严格稳定分布与正态分布和指数分布,发现PPS分布更适合拟合保险数据。在基金分离理论下,从风险厌恶型投资者的视角,在非正态稳定分布条件下研究多期投资组合模型。研究了非正态稳定分布条件下市场上含有多个风险证券和一个无风险证券时的多期投资组合,建立了多期投资组合模型；加入新的假设,对模型进行改进,并对模型的求解及其应用条件进行分析；用美国股票收益率数据进行实证研究,给出多支股票多期投资组合的最优投资组合策略。
[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.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O211.3;F830.59

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