几类风险模型下第n次索赔的破产概率研究
发布时间：2019-05-07 16:59
【摘要】：近年来,风险理论发展十分迅速,众多学者致力于保险公司破产概率的研究,涌现出很多新的风险模型,丰富和完善了风险理论；大部分学者对破产概率的研究主要集中于对破产时间、破产前瞬间盈余、破产时刻赤字等变量的研究,很少有学者对破产索赔次数与破产时间之间的关系进行研究；因此,将索赔次数和破产时间放在一起研究是一个比较新的,有意义的课题,一些关于破产时间的已知结果可以用破产时的索赔次数来解释；研究不同风险模型下第n次索赔的破产概率具有一定的理论价值和现实指导意义,是一个非常有意义的课题。 本文首先介绍了风险理论的一些基本的知识和方法；然后为了使风险模型更符合实际情况,在经典风险模型的基础上,研究了风险事件不等同于索赔事件的Poisson-Geometric风险模型；通过构造一类Gerber-Shiu函数,分别推导出该风险模型下Gerber-Shiu函数满足的更新方程,破产时刻和直到破产时的索赔次数的联合密度函数,最终得到了第n次索赔时的破产概率的数学表达式。又考虑到经典风险模型中,保险公司只面对单风险的情形,但现实生活中,保险公司会承担不同的保险业务；因此,本文又研究了独立二元风险模型和一类索赔相依的二元风险模型的破产问题,最终得到了这两种风险模型下第n次索赔时的破产概率的数学表达式。 最后,对本文的研究结果作了一个总结,给出了本文的展望。
[Abstract]:In recent years, the risk theory develops very rapidly, many scholars devote to the insurance company bankruptcy probability research, emerged many new risk models, enriched and perfected the risk theory; The majority of scholars mainly focus on the bankruptcy time, the instant surplus before bankruptcy, the deficit at the ruin time and so on. Few scholars study the relationship between the number of bankruptcy claims and the bankruptcy time, and few scholars study the relationship between the number of bankruptcy claims and the bankruptcy time. Therefore, the study of the number of claims and the time of bankruptcy together is a relatively new and meaningful subject, and some known results about the time of bankruptcy can be explained by the number of claims at the time of bankruptcy; The research on the ruin probability of the nth claim under different risk models has certain theoretical value and practical guiding significance, and it is a very meaningful subject. This paper first introduces some basic knowledge and methods of risk theory, and then, in order to make the risk model more suitable to the actual situation, on the basis of the classical risk model, studies the Poisson-Geometric risk model of risk event which is not equal to the claim event; By constructing a class of Gerber-Shiu function, the renewal equation of Gerber-Shiu function under the risk model, the joint density function of the time of ruin and the number of claims until ruin are derived, respectively. Finally, the mathematical expression of the ruin probability of the nth claim is obtained. Taking into account the classical risk model, insurance companies only face the case of single risk, but in real life, insurance companies will assume different insurance business; Therefore, the ruin problem of independent dualistic risk model and a kind of dependent dualistic risk model is studied in this paper. Finally, the mathematical expression of the ruin probability of the nth claim under these two risk models is obtained. Finally, the research results of this paper are summarized, and the prospect of this paper is given.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840;F224
[Abstract]:In recent years, the risk theory develops very rapidly, many scholars devote to the insurance company bankruptcy probability research, emerged many new risk models, enriched and perfected the risk theory; The majority of scholars mainly focus on the bankruptcy time, the instant surplus before bankruptcy, the deficit at the ruin time and so on. Few scholars study the relationship between the number of bankruptcy claims and the bankruptcy time, and few scholars study the relationship between the number of bankruptcy claims and the bankruptcy time. Therefore, the study of the number of claims and the time of bankruptcy together is a relatively new and meaningful subject, and some known results about the time of bankruptcy can be explained by the number of claims at the time of bankruptcy; The research on the ruin probability of the nth claim under different risk models has certain theoretical value and practical guiding significance, and it is a very meaningful subject. This paper first introduces some basic knowledge and methods of risk theory, and then, in order to make the risk model more suitable to the actual situation, on the basis of the classical risk model, studies the Poisson-Geometric risk model of risk event which is not equal to the claim event; By constructing a class of Gerber-Shiu function, the renewal equation of Gerber-Shiu function under the risk model, the joint density function of the time of ruin and the number of claims until ruin are derived, respectively. Finally, the mathematical expression of the ruin probability of the nth claim is obtained. Taking into account the classical risk model, insurance companies only face the case of single risk, but in real life, insurance companies will assume different insurance business; Therefore, the ruin problem of independent dualistic risk model and a kind of dependent dualistic risk model is studied in this paper. Finally, the mathematical expression of the ruin probability of the nth claim under these two risk models is obtained. Finally, the research results of this paper are summarized, and the prospect of this paper is given.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840;F224
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