基于金融、保险领域的重尾现象研究

发布时间：2018-01-25 17:41

本文关键词： 重尾现象尾部相关性二维风险模型破产概率相依结构　出处：《浙江工商大学》2014年硕士论文　论文类型：学位论文

【摘要】：本文以重尾现象为主线,采用实证分析和理论分析相结合的方法,主要对金融领域和保险领域中的重尾现象进行研究。文章首先介绍了相应的理论基础,之后在第五章中主要研究金融领域的重尾现象,以实证分析为主,选取中、美股票市场八个行业的股指收益率数据作为研究对象,首先通过图表展示和重尾指数对比分析,定性、定量描述了各行业、两国股市收益率数据的重尾特征,之后对相同行业两国股市股指收益率间的尾部相关性进行研究；采用时变SJC Copula作为主要研究工具,引入股市映射效应概念,同时考虑金融危机影响因素,以危机的发生和消散为时间节点,将数据分成三个阶段分别讨论,经分析得出如下结论：能源、工业和金融三组行业,左侧尾部相关性高于右侧；基础材料行业右侧尾部相关性高于左侧；消费者常用品行业仅存在左侧尾部相关性；医药行业尾部相关性较低；电信服务和公用事业行业不存在尾部相关性。存在相关性的六组行业中,美国股市对我国股市普遍具有左尾映射效应,我国股市对美国股市没有映射效应；金融危机的到来使得两国股市相关性发生变化,总体上促使我国股市向着美国成熟股市方向发展。文章第六章研究保险领域中的重尾现象,以理论分析为主,在经典风险模型基础上,假设保险公司索赔额服从局部次指数分布,构建了局部Max-Sum等价式,并给予相应证明；随后,重点探究相依结构下非标准二维更新风险模型的破产概率问题,假设两类索赔额随机变量服从重尾分布、索赔到达时刻相同,并且在Farlie-Gumbel-Morgenstern结构基础上,构建了两个Copula相依结构,在索赔额序列与索赔来到时间间隔序列服从这两个相依结构时,推导出有限时破产概率的两类渐近等价式。
[Abstract]:This paper takes the heavy-tailed phenomenon as the main line, and mainly studies the heavy-tailed phenomenon in the field of finance and insurance by the method of combining empirical analysis with theoretical analysis. The article first introduces the corresponding theoretical basis, and then in the 5th chapter mainly studies the heavy-tailed phenomenon in the financial field, mainly in the empirical analysis, select. The stock index yield data of eight industries in the United States stock market as the research object, first through the chart display and heavy-tailed index comparative analysis, qualitative and quantitative description of each industry, the two countries stock market yield data heavy-tailed characteristics. Then the tail correlation between stock index yield of the same industry and two countries is studied. Using time-varying SJC Copula as the main research tool, this paper introduces the concept of stock market mapping effect, and takes the occurrence and dissipation of financial crisis as the time node. The data are divided into three stages, and the conclusions are as follows: energy, industry and finance are the three groups of industries, the left tail correlation is higher than the right; The correlation between the right side and the tail is higher than that on the left side. There is only the left tail correlation in the industry of common consumer products; The tail correlation of pharmaceutical industry is low; There is no tail correlation between telecom service and public utility industry. In the six groups of industries with correlation, the American stock market has the left-tail mapping effect to our stock market, and the Chinese stock market has no mapping effect to the American stock market. The arrival of the financial crisis has changed the correlation between the stock markets of the two countries and promoted the stock market of our country to develop towards the mature stock market of the United States. Chapter 6th studies the heavy-tailed phenomenon in the field of insurance. Based on the classical risk model, it assumes that the insurance company claims the amount from the local sub-exponential distribution. The local Max-Sum equivalent formula is constructed and proved. Then, we focus on the ruin probability of the non-standard two-dimensional renewal risk model under the dependent structure, assuming that the two kinds of random variables of claim amount are distributed from heavy tail, and the arrival time of the claim is the same. On the basis of Farlie-Gumbel-Morgenstern structure, two Copula dependent structures are constructed. When the sequence of claim amount and the sequence of claim arrival time are dependent on these two dependent structures, two classes of asymptotic equivalent formulas for the ruin probability of finite time are derived.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F831.51;F841;F224

【相似文献】