几类广义复合二项风险模型的破产问题研究
发布时间：2018-08-27 19:52
【摘要】：经典的二项风险模型是精算文献中研究得最深入的离散时间更新风险过程,近些年来,许多精算学者从不同的方面把经典二项风险模型进行了推广,得到了许多有价值的结论.在经典的复合二项风险模型的基础上,本文研究几类广义复合二项风险模型,并且对这些模型的破产概率做了深入研究. 本论文共分为五章： 第一章本章首先对风险理论及其核心内容破产理论作简要介绍,然后对经典复合二项风险模型做了综合性的回顾,最后介绍了本文的主要工作. 第二章本章研究具有一般保费率的CCBM的破产概率,即索赔次数过程为一个复合二项过程,而保费率为一个非负整数.我们得到了该模型下最终破产概率的表达式和相应的上界估计. 第三章本章研究保费收入为复合二项过程的CCBM的破产概率,即假设保费收取次数服从复合二项分布,而索赔次数过程为一个复合复合二项过程,保费率为1,用鞅方法研究该模型下最终破产概率的表达式和相应的上界估计. 第四章本章研究保费收入为复合二项过程的带扰动CCBM的破产概率,在前一章的基础上考虑投资与干扰的因素,假设保费收取次数服从复合二项分布,而索赔次数过程为一个复合复合二项过程,建立一种贴近现实的新模型,得到最终破产概率的表达式和相应的上界估计. 第五章本章研究保费收入为复合二项过程的带投资和扰动CCBM的破产概率,在上一章模型的基础上考虑到投资利率和通货膨胀等一些干扰因素对保险公司经营状态影响,用鞅方法研究该模型下最终破产概率的表达式和相应的上界估计.
[Abstract]:The classical binomial risk model is the most deeply studied discrete time renewal risk process in the actuarial literature. In recent years, many actuarial scholars have extended the classical binomial risk model from different aspects and obtained many valuable conclusions. On the basis of classical compound binomial risk models, several generalized compound binomial risk models are studied in this paper, and the ruin probability of these models is studied deeply. This paper is divided into five chapters: the first chapter briefly introduces the risk theory and its core theory of bankruptcy, then makes a comprehensive review of the classical compound binomial risk model, and finally introduces the main work of this paper. In chapter 2, we study the ruin probability of CCBM with general premium rate, that is, the process of claim number is a compound binomial process, and the premium rate is a non-negative integer. We obtain the expression of the final ruin probability and the corresponding upper bound estimate. In Chapter 3, we study the ruin probability of CCBM, where the premium income is a compound binomial process, that is, assuming that the premium collection times are distributed from the compound binomial, and the claim number process is a compound binomial process. The premium rate is 1. The expression of the final ruin probability and the corresponding upper bound estimate are studied by martingale method. In chapter 4, we study the ruin probability of perturbed CCBM with a compound binomial process. On the basis of the previous chapter, we consider the factors of investment and disturbance, and assume that the premium collection times are distributed by compound binomial. The process of claim number is a compound binomial process. A new model close to reality is established, and the expression of the final ruin probability and the corresponding upper bound estimate are obtained. In chapter 5, we study the ruin probability with investment and perturbed CCBM when the premium income is a compound binomial process. On the basis of the model in the previous chapter, we consider the influence of some factors such as investment interest rate and inflation on the operating state of the insurance company. The expression of final ruin probability and the corresponding upper bound estimate are studied by martingale method.
【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.4;F224
本文编号：2208289
[Abstract]:The classical binomial risk model is the most deeply studied discrete time renewal risk process in the actuarial literature. In recent years, many actuarial scholars have extended the classical binomial risk model from different aspects and obtained many valuable conclusions. On the basis of classical compound binomial risk models, several generalized compound binomial risk models are studied in this paper, and the ruin probability of these models is studied deeply. This paper is divided into five chapters: the first chapter briefly introduces the risk theory and its core theory of bankruptcy, then makes a comprehensive review of the classical compound binomial risk model, and finally introduces the main work of this paper. In chapter 2, we study the ruin probability of CCBM with general premium rate, that is, the process of claim number is a compound binomial process, and the premium rate is a non-negative integer. We obtain the expression of the final ruin probability and the corresponding upper bound estimate. In Chapter 3, we study the ruin probability of CCBM, where the premium income is a compound binomial process, that is, assuming that the premium collection times are distributed from the compound binomial, and the claim number process is a compound binomial process. The premium rate is 1. The expression of the final ruin probability and the corresponding upper bound estimate are studied by martingale method. In chapter 4, we study the ruin probability of perturbed CCBM with a compound binomial process. On the basis of the previous chapter, we consider the factors of investment and disturbance, and assume that the premium collection times are distributed by compound binomial. The process of claim number is a compound binomial process. A new model close to reality is established, and the expression of the final ruin probability and the corresponding upper bound estimate are obtained. In chapter 5, we study the ruin probability with investment and perturbed CCBM when the premium income is a compound binomial process. On the basis of the model in the previous chapter, we consider the influence of some factors such as investment interest rate and inflation on the operating state of the insurance company. The expression of final ruin probability and the corresponding upper bound estimate are studied by martingale method.
【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.4;F224
【参考文献】
相关期刊论文 前2条
1 龚日朝;邹捷中;;复合二项风险模型下Gerber-Shiu折现惩罚函数的渐近解[J];系统科学与数学;2007年04期
2 彭丹;侯振挺;刘再明;;随机利率下相依索赔的离散风险模型的分红问题[J];应用数学学报;2011年06期
，本文编号：2208289
本文链接：https://www.wllwen.com/jingjilunwen/bxjjlw/2208289.html
