两类多维风险模型有限时间破产概率的一致渐近性

发布时间：2018-02-10 00:41

本文关键词： 一致渐近性布朗运动相依有限时间破产概率　出处：《曲阜师范大学》2014年硕士论文　论文类型：学位论文

【摘要】：本文考虑了两类带布朗运动干扰和常利率的n维更新风险模型有限时间的破产概率的一致渐近性.其中一类风险模型中的n种索赔来到的时间是不同的;另一类的n种索赔来到的时间是相同的.在这两类n维风险模型中, n种索赔的索赔额的大小是上尾渐近独立(英文简写为UTAI,见定义2.4)的随机变量,它们的分布函数同时属于长尾分布类(见定义2.2)和主导变化尾分布类(见定义2.2),而且来到时间间隔服从广义下限相依结构(英文简写为WLOD,见定义2.3). 本文所讨论的两类n维更新风险模型，，其中的一类可以表示一个保险公司有n种不同的保险业务且这些保险业务的索赔来到时刻是不相同的;而另外一类可以表示一个保险公司的n种不同的保险业务的索赔来到时刻是相同的.本文的主要目的是研究这两类风险模型的三种有限时间的破产概率的一致渐近性.我们定义了三种多维的非标准的更新风险模型的破产时.这三种破产时分别是:一、保险公司中的每一个业务的盈余都达到负值的最小时间;二、保险公司中至少有一个业务的盈余达到负值的最小时间;三、保险公司中的所有业务盈余的和值达到负值的最小时间.对应每一种破产时我们相应的定义了一种破产概率.最后,我们得到了这三种有限时间破产概率的一致渐近性. 根据文章的主要内容,本文可分为以下五章:第一章描述了本文所要研究的两类多维风险模型;第二章的预备知识主要介绍了本文中所用到的定义和一些背景;在第三章中给出了本文的一些结果;在第四章中我们给出了一些引理;最后是主要结果的证明.
[Abstract]:In this paper, we consider the uniform asymptotic behavior of ruin probability for two classes of n-dimensional renewal risk models with Brownian motion disturbance and constant interest rate. In these two types of n-dimensional risk models, the claim amount of n claims is a random variable whose upper tail is asymptotically independent (UTAI, see definition 2.4). Their distribution functions belong to both the long-tailed distribution class (see definition 2.2) and the dominant variable-tail distribution class (see definition 2.2), and come to the interval from the generalized lower bound dependent structure (WLOD). In this paper, two classes of n-dimensional renewal risk models are discussed, one of which can indicate that an insurance company has n different types of insurance business and the claims for these insurance services are different at the time of arrival. The other kind of claim that can represent n different kinds of insurance business of an insurance company is at the same time. The main purpose of this paper is to study the consistency of ruin probability of three kinds of finite time of these two kinds of risk models. Nearness. We define the ruin time of three multidimensional non-standard renewal risk models. The three kinds of ruin time are as follows: 1. The minimum time for each business surplus in an insurance company to be negative; second, for at least one business in an insurance company to reach a negative value; third, The minimum time for the sum of all the business surpluses in insurance companies to be negative. For each ruin we define a ruin probability. Finally we obtain the uniform asymptotic property of the three finite time ruin probabilities. According to the main contents of this paper, this paper can be divided into the following five chapters: the first chapter describes the two kinds of multi-dimensional risk models to be studied in this paper, the second chapter introduces the definitions and some background used in this paper. In the third chapter, we give some results of this paper; in Chapter 4th, we give some lemmas; finally, we prove the main results.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O211.6;F840.31

【参考文献】