几类复合二项风险模型破产概率的研究

发布时间：2018-04-06 05:12

本文选题：退保　切入点：投资收益　出处：《河南理工大学》2014年硕士论文

【摘要】：本文在前人研究的经典风险模型的基础上,综合实际情况加入退保、投资以及干扰等因素,将保险公司的保费收取过程和理赔发生过程进行推广,讨论了三类有关二项风险模型的破产概率.第一部分,给出本文研究的背景即风险理论以及破产概率相关知识.本部分分两章,第一章主要介绍了破产理论的发展历程,对破产理论有一个大概的了解.然后介绍经典风险模型的研究及推广.第二章主要介绍了与二项风险模型相关的一些知识,如点过程、鞅论等,为下面的研究打下基础.第二部分,几类二项风险模型的讨论.本部分由三章节组成,在经典模型的研究基础上,首先第三章主要讨论了考虑退保因素的一类风险模型,建立新的模型后得出一些重要结论.第四章在考虑投资收益的基础上研究了一类双险种的复合二项风险模型,得到模型的破产概率表达式及Lundberg不等式.第五章在前两类模型的基础上加入干扰因素,利用收敛定理和鞅分析方法,研究了带干扰的多险种风险模型,得出了最终破产概率.
[Abstract]:On the basis of the classical risk model studied by the predecessors, the insurance company's premium collection process and claim recovery process are generalized by adding the factors such as withdrawal, investment and interference into the actual situation.The ruin probability of three classes of binomial risk models is discussed.In the first part, the background of this paper, risk theory and ruin probability knowledge, are given.This part is divided into two chapters. The first chapter mainly introduces the development of bankruptcy theory, and has a general understanding of bankruptcy theory.Then it introduces the research and extension of classical risk model.The second chapter mainly introduces some knowledge related to binomial risk model, such as point process, martingale theory and so on, which lays a foundation for the following research.In the second part, several kinds of binomial risk models are discussed.This part is composed of three chapters. On the basis of the classical model, the third chapter mainly discusses a kind of risk model considering the factors of retreat, and draws some important conclusions after the establishment of the new model.In chapter 4, we study a kind of compound binomial risk model based on investment return, and obtain the ruin probability expression and Lundberg inequality of the model.In the fifth chapter, the interference factors are added to the first two kinds of models. By using convergence theorem and martingale analysis method, the multi-insurance risk model with interference is studied, and the final ruin probability is obtained.
【学位授予单位】：河南理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O211.67;F840

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