关于保险与金融中重尾现象的若干研究

发布时间：2018-10-24 20:40

【摘要】：重尾现象对于我们来说已经不再陌生,它几乎出现在所有领域中,保险公司的索赔额、金融时间序列数据、网络流量、自然气象数据以及大部分人类行为数据的分布形态都表现出尖峰厚尾的特征。重尾现象的极端形态表现为极端事件,是指那些意料之外,但一旦发生,往往导致巨大的影响,甚至产生极其严重的后果的事件。对于重尾现象,我们一般用重尾分布来刻画。所谓重尾,本质上是刻画一个分布的尾部趋于零的速度。直观上,当这个速度慢于任意的指数速度时,该分布就是重尾的。稳定分布因具有类似于现实实证分布的前段指数,后端幂律的形式,对重尾现象的刻画具有较理想的拟合效果。本文主要是从多个角度围绕重尾现象进行研究,首先对保险领域和金融领域中的重尾现象进行研究。在保险领域讨论了重尾索赔对保险公司的经营稳健性影响,比较了索赔额服从指数分布和Pareto、 Frechet、Weibull分布时的破产概率。在金融领域讨论了重尾场合下金融市场的风险度量,认为传统方法在估计VaR值时存在缺陷,而运用极值理论能更好的估计VaR。接着,从不同理论视角(流动性黑洞视角、非线性视角)讨论了重尾现象,通过正反馈机制、非线性对重尾现象进行机理上的探究。最后,本文介绍了关于重尾现象的统计学描述方法,利用稳定分布来拟合上证指数日收益数据,取得较好的拟合效果。本文分为六章,研究内容如下：第一章,导论。介绍了选题背景、意义及相关文献并阐述了论文的研究内容和方法,对论文的创新之处与不足之处做了说明。第二章,重尾索赔下保险公司的经营稳健性分析。在讨论了重尾索赔对保险公司的经营稳健性影响,比较了索赔额服从指数分布和Pareto、Frechet、Weibull分布时的破产概率。第三章,重尾场合下金融市场的风险度量研究。讨论了传统方法估计VaR值的缺陷,认为极值理论在重尾场合下能更好的估计VaR。第四章,重尾现象的统计学描述方法。介绍了重尾分布、稳定分布并推导了稳定分布的特征函数解析式。第五章,重尾现象的稳定分布拟合。以上证指数日收益数据为例,对其进行重尾检测,用稳定分布来拟合收益序列,取得较好的拟合效
[Abstract]:The heavy-tailed phenomenon is no stranger to us, it appears in almost all areas, insurance claims, financial time series data, network traffic, The distribution patterns of natural meteorological data and most human behavior data all show the characteristics of peak and thick tail. The extreme form of heavy-tailed phenomenon is characterized by extreme events, which are unexpected, but once they occur, they often lead to great influence and even extremely serious consequences. For heavy-tailed phenomenon, we generally describe it by heavy-tailed distribution. A heavy tail is essentially a description of the velocity at which the tail of a distribution tends to zero. Intuitively, when this velocity is slower than any exponential velocity, the distribution is heavy-tailed. The stable distribution is similar to the real empirical distribution in the form of the front exponent and the back-end power law, so the characterization of the heavy-tailed phenomenon has a better fitting effect. This paper mainly studies the heavy-tailed phenomenon from many angles, first of all, it studies the heavy-tailed phenomenon in the insurance and financial fields. In the field of insurance, the influence of heavy-tailed claims on the business stability of insurance companies is discussed, and the ruin probability is compared between exponential distribution and Pareto, Frechet,Weibull distribution. This paper discusses the risk measurement of financial market in the field of finance, and points out that the traditional method has some defects in estimating the VaR value, and the extreme value theory can better estimate the VaR.. Then, the heavy-tailed phenomenon is discussed from different theoretical perspectives (liquidity black hole perspective, nonlinear perspective), and the mechanism of heavy-tailed phenomenon is explored through positive feedback mechanism. Finally, this paper introduces the statistical description method of heavy-tailed phenomenon. The stable distribution is used to fit the daily income data of Shanghai Stock Exchange Index, and a good fitting effect is obtained. This paper is divided into six chapters, the research content is as follows: the first chapter, introduction. This paper introduces the background, significance and related literature of the selected topic, expounds the research contents and methods of the thesis, and explains the innovation and deficiency of the paper. The second chapter, the heavy tail claims under the insurance company's business stability analysis. In this paper, we discuss the influence of heavy-tailed claims on the business robustness of insurance companies, and compare the ruin probability of claims with exponential distribution and Pareto,Frechet,Weibull distribution. Chapter three, the risk measurement research of financial market under the circumstance of heavy end. This paper discusses the defects of traditional method in estimating VaR value, and holds that extreme value theory can better estimate VaR. in heavy-tailed cases. Chapter 4, the statistical description of heavy-tailed phenomenon. The heavy-tailed distribution and the stable distribution are introduced and the analytic expressions of the eigenfunction of the stable distribution are derived. Chapter 5, steady distribution fitting of heavy-tailed phenomenon. Taking the daily income data of Shanghai stock index as an example, the heavy-tailed test is carried out, and the stable distribution is used to fit the income sequence, and a good fitting effect is obtained.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840;F830;F224

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