几类重尾风险模型破产概率的研究

发布时间：2018-05-23 17:12

本文选题：重尾分布 + 破产概率　；参考：《华东师范大学》2014年博士论文

【摘要】：在保险精算中,有些极端事件,比如洪灾、地震、火山喷发等,一旦发生就会对保险公司产生严重的冲击,造成保险公司运营困难,有的甚至导致其破产.而且近年来这类事件也频繁发生.因此人们越来越重视对重尾理赔额所驱动的风险过程的研究.鉴于此,本文考虑了几类重尾风险模型.具体内容如下： 1.第一章首先阐述了本文的研究背景.接着,介绍了常见的重尾分布族.然后,介绍了标准更新风险模型及破产概率的定义.最后,给出了一些基本概念和定理及本论文的主要工作. 2.第二章研究了带投资的二维风险模型的破产概率.考虑同一家保险公司的两种不同险种的索赔同时到达的情况.在二维框架下研究了两种类型的破产.利用鞅方法得到了最终破产概率的上界.对于这两种类型的破产分别得到了生存概率满足的积分-微分方程,以及有限时间破产概率的渐近表达式. 3.第三章考虑了带常利率的二维风险模型的破产概率.在本章的模型中,每一次索赔是由两家保险公司按一定的比例来支付.在二维框架下研究了两种类型的破产,对于这两种类型的破产分别得到了生存概率满足的积分-微分方程,以及有限时间破产概率的渐近表达式. 4.第四章研究了带常利率的复合泊松风险模型的Gerber-Shiu罚金函数和破产概率.得到了罚金函数满足的积分-微分方程.从而得到了破产概率满足的积分-微分方程.由此出发还得到了破产概率的渐近表达式. 5.第五章考虑了随机保费收入风险模型破产概率的一致渐近性.得到了有限时破产概率和最终破产概率的渐近表达式,并且获得的渐近表达式对时间一致成立. 6.第六章研究了带随机利率的离散时间风险模型的破产概率.在索赔额的分布属于D∩L族的条件下,得到了最终破产概率的渐近表达式.
[Abstract]:In actuarial insurance, some extreme events, such as floods, earthquakes, volcanic eruptions and so on, will have a serious impact on insurance companies once they occur, resulting in the operation of insurance companies difficult, some even lead to bankruptcy. And in recent years, such incidents have occurred frequently. Therefore, people pay more and more attention to the risk process driven by heavy-tailed claims. In view of this, several kinds of heavy tail risk models are considered in this paper. The details are as follows: 1. The first chapter describes the background of this paper. Then, the common heavy-tailed distribution family is introduced. Then, the standard renewal risk model and the definition of ruin probability are introduced. Finally, some basic concepts and theorems are given, as well as the main work of this paper. 2. In chapter 2, the ruin probability of two-dimensional risk model with investment is studied. Consider the simultaneous arrival of claims for two different types of insurance from the same insurance company. Two types of bankruptcy are studied in a two-dimensional framework. The upper bound of the final ruin probability is obtained by using martingale method. For these two types of ruin, the asymptotic expressions of the integro-differential equation satisfying the survival probability and the ruin probability of finite time are obtained respectively. 3. In chapter 3, the ruin probability of two-dimensional risk model with constant interest rate is considered. In the model of this chapter, each claim is paid by two insurance companies in proportion. In this paper, two types of ruin are studied in a two-dimensional framework. For these two types of ruin, the integro-differential equations satisfying the survival probability and the asymptotic expression of the ruin probability in finite time are obtained, respectively. 4. In chapter 4, the Gerber-Shiu penalty function and ruin probability of compound Poisson risk model with constant interest rate are studied. The integro-differential equation satisfying the fine function is obtained. Thus, the integro-differential equation satisfying the ruin probability is obtained. The asymptotic expression of ruin probability is also obtained. 5. In chapter 5, we consider the uniform asymptotic property of ruin probability of stochastic premium income risk model. The asymptotic expressions of finite ruin probability and final ruin probability are obtained, and the obtained asymptotic expressions are consistent with time. 6. In chapter 6, the ruin probability of discrete time risk model with stochastic interest rate is studied. The asymptotic expression of the final ruin probability is obtained under the condition that the distribution of the claim amount belongs to the D class of L.
【学位授予单位】：华东师范大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F224;F840

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