重尾分布及其在风险模型破产概率估计中的研究
发布时间：2018-12-13 23:00
【摘要】：破产理论是精算数学领域的一个重要部分,它不仅具有重要的理论研究价值,而且在金融保险公司风险管理中有极强的实用价值。保险业作为金融业四大支柱之一,其本身也面临索赔风险,特别是对公司的经营状况有重大影响的“大额索赔”情形,此类索赔在数学上用重尾分布来刻画。经典的Lundberg-Cramer风险模型是不考虑利息力因素的影响,但是在现实市场经济环境下利息力对投资者决策及其投资行为心理有重要影响,是保险公司必须要考虑的一个重要因素。 本论文的研究内容是在重尾索赔下考虑利息力因素的离散时间风险模型的破产概率。全文分为5章： 第1章是绪论,主要概述了破产理论的发展历史,介绍了Lundberg-Cramer经典风险模型,并归纳了学者们推广与改进的风险模型,最后总结了当代破产理论几个具有代表性的研究方向。 第2章是重尾分布及其子族,主要介绍了重尾分布的定义、重尾子族的划分及重尾子族之间的相互关系。 第3章考虑了带变利息力的离散时间风险模型,将风险模型通过盈余折现变形,假设个体净风险服从D∩L族和εRV族,分别得到有限时间和无限时间破产概率的一致尾等价关系式及其上下界表达式。 第4章考虑的是带Markov链利息力的离散时间风险模型,在个体净风险服从R-α族和相关重尾假设下,利用全概率公式和递推方法,得到有限时间离散风险模型破产概率的近似表达式。 第5章对全文的研究结果做了总结,并介绍了作者下一步的工作计划。
[Abstract]:Bankruptcy theory is an important part in the field of actuarial mathematics. It not only has important theoretical research value, but also has a strong practical value in risk management of financial insurance companies. As one of the four pillars of the financial industry, the insurance industry itself also faces the risk of claim, especially the "large claim" situation, which has a significant impact on the company's operating conditions. This kind of claim is mathematically characterized by heavy-tailed distribution. The classical Lundberg-Cramer risk model does not consider the influence of interest force, but in the real market economy, interest force has an important influence on investors' decision-making and investment behavior psychology, which is an important factor that insurance companies must consider. In this paper, the ruin probability of discrete-time risk model with interest force is considered in heavy-tailed claims. The thesis is divided into five chapters: the first chapter is the introduction, which summarizes the development history of bankruptcy theory, introduces the classical risk model of Lundberg-Cramer, and summarizes the risk model which is popularized and improved by scholars. Finally, several representative research directions of contemporary bankruptcy theory are summarized. In chapter 2, we introduce the definition of heavy-tailed distribution, the division of heavy-tailed sub-family and the relationship between heavy-tailed subfamilies. In chapter 3, the discrete time risk model with variable interest force is considered, and the risk model is deformed by surplus. The uniform tail equivalent relation and its upper and lower bound expressions of the ruin probability of finite time and infinite time are obtained respectively. In chapter 4, the discrete time risk model with interest force of Markov chain is considered. Under the assumption of R- 伪 family and related heavy tail, the full probability formula and recursive method are used. The approximate expression of ruin probability of finite time discrete risk model is obtained. Chapter 5 summarizes the research results and introduces the author's next work plan.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;O211.3
本文编号：2377405
[Abstract]:Bankruptcy theory is an important part in the field of actuarial mathematics. It not only has important theoretical research value, but also has a strong practical value in risk management of financial insurance companies. As one of the four pillars of the financial industry, the insurance industry itself also faces the risk of claim, especially the "large claim" situation, which has a significant impact on the company's operating conditions. This kind of claim is mathematically characterized by heavy-tailed distribution. The classical Lundberg-Cramer risk model does not consider the influence of interest force, but in the real market economy, interest force has an important influence on investors' decision-making and investment behavior psychology, which is an important factor that insurance companies must consider. In this paper, the ruin probability of discrete-time risk model with interest force is considered in heavy-tailed claims. The thesis is divided into five chapters: the first chapter is the introduction, which summarizes the development history of bankruptcy theory, introduces the classical risk model of Lundberg-Cramer, and summarizes the risk model which is popularized and improved by scholars. Finally, several representative research directions of contemporary bankruptcy theory are summarized. In chapter 2, we introduce the definition of heavy-tailed distribution, the division of heavy-tailed sub-family and the relationship between heavy-tailed subfamilies. In chapter 3, the discrete time risk model with variable interest force is considered, and the risk model is deformed by surplus. The uniform tail equivalent relation and its upper and lower bound expressions of the ruin probability of finite time and infinite time are obtained respectively. In chapter 4, the discrete time risk model with interest force of Markov chain is considered. Under the assumption of R- 伪 family and related heavy tail, the full probability formula and recursive method are used. The approximate expression of ruin probability of finite time discrete risk model is obtained. Chapter 5 summarizes the research results and introduces the author's next work plan.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;O211.3
【参考文献】
相关期刊论文 前5条
1 陈琳;刘维奇;;重尾分布族及其关系图[J];高校应用数学学报A辑;2009年02期
2 尹传存;关于破产概率的一个局部定理[J];中国科学(A辑:数学);2004年02期
3 张帆;;利率为Markov链的风险模型的破产问题[J];山西大学学报(自然科学版);2009年02期
4 苏淳,胡治水,唐启鹤;关于非负分布重尾程度的刻画[J];数学进展;2003年05期
5 金士伟;;索赔额是指数分布的马氏风险模型的破产概率[J];运筹学学报;2010年01期
，本文编号：2377405
本文链接：https://www.wllwen.com/jingjilunwen/bxjjlw/2377405.html
