随机保费收入情形下相依更新风险模型的期望折现罚金函数研究
发布时间：2019-02-13 06:11
【摘要】：对于经典风险模型的研究,都是基于保费收入是线性增长和理赔过程是Poisson的这两个重要的假设条件之下。但是随着保险业的发展,我们发现在实际运营过程中,这些条件与保险公司当前的实际情况越来越不符合。因此,研究出一个更为贴近保险公司实务的风险模型成为了当代精算学者们的当务之急。许多精算学者投入了大量的精力,并取得了丰硕的成果。 本文就是在继承前人的研究成果之上,综合考虑对保费收入和对理赔过程两种类型的推广,主要构建了两种非线性的保费收入的相依风险模型,使得模型更贴近保险实务。并通过运用复分析、随机过程以及风险理论等学科理论知识来研究了这两类模型的期望折现罚金函数的计算方法。本文的内容框架如下： 第一章首先对经典风险模型以及它所具备的特征作了简单的介绍；其次,结合本文的主要研究内容,我们简要回顾了目前国内外相关方面的研究现状；最后介绍本文的主要研究内容。 第二章首先给出了若干约定；其次结合本文理论研究过程的需要,给出了一些研究过程中所涉及的相关知识以及研究所需的工具方法。 第三章通过将保费收入过程从经典风险模型中的线性增长推广到非线性的Poisson过程,以及考虑到理赔过程中理赔间隔时间与理赔额之间实际中应存在着一定的依赖关系,构建了Poisson保费收入的一类相依情形下的更新风险模型,其中保费收入是Poisson的,且理赔间隔时间与理赔额之间的依赖关系满足Boudreault et alo.(2006)中所提出的依赖关系。此外,本章讨论了该模型下的Gerber-Shiu函数的计算方法,并成功推导出其生成函数的精确表达式,并且得到了生成函数所满足的瑕疵更新方程的显示表达式。 第四章,我们在第三章的研究基础之上把保费收入过程进一步推广到复合Poisson过程的相依更新风险模型。其所满足的相依关系依然是Boudreault et al.(2006)中提出的。本章通过考虑首次理赔间隔时间和首次发生保费收入的到达时刻之间的关系,推导出此相依情形下的Gerber-Shiu函数的Laplace变换的显示表达式.
[Abstract]:The study of classical risk model is based on the assumption that premium income is linear growth and claim process is Poisson. However, with the development of insurance industry, we find that these conditions are more and more inconsistent with the actual situation of insurance companies. Therefore, to develop a risk model closer to the practice of insurance companies has become an urgent task for modern actuaries. Many actuaries have invested a great deal of energy and achieved fruitful results. In this paper, based on the previous research results, we consider the generalization of premium income and claim process synthetically, and construct two nonlinear risk models of premium income, which make the model more close to insurance practice. By using the knowledge of complex analysis, stochastic process and risk theory, this paper studies the calculation method of the expected discounted penalty function of these two kinds of models. The main contents of this paper are as follows: the first chapter introduces the classical risk model and its characteristics. Secondly, combined with the main research content of this paper, we briefly review the current research situation at home and abroad, and finally introduce the main research content of this paper. In the second chapter, some conventions are given first, and then some relevant knowledge and tools are given according to the needs of the theoretical research process in this paper. The third chapter extends the premium income process from the linear growth in the classical risk model to the nonlinear Poisson process, and considers that there should be a certain dependence between the claim interval and the amount of claim in the process of settlement. In this paper, an update risk model of Poisson premium income is constructed, in which the premium income is Poisson, and the dependence between claim interval and claim amount satisfies the dependency proposed in Boudreault et alo. (2006). In addition, this chapter discusses the calculation method of the Gerber-Shiu function under the model, and successfully deduces the exact expression of the generating function, and obtains the display expression of the defective update equation satisfied by the generating function. In Chapter 4, we extend the premium income process to the dependent renewal risk model of the compound Poisson process based on the research in Chapter 3. The dependent relation it satisfies is still proposed in Boudreault et al. (2006). In this chapter, by considering the relationship between the interval between the first claim and the arrival time of the first premium income, the expression of the Laplace transform of the Gerber-Shiu function in this dependent case is derived.
【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
本文编号：2421261
[Abstract]:The study of classical risk model is based on the assumption that premium income is linear growth and claim process is Poisson. However, with the development of insurance industry, we find that these conditions are more and more inconsistent with the actual situation of insurance companies. Therefore, to develop a risk model closer to the practice of insurance companies has become an urgent task for modern actuaries. Many actuaries have invested a great deal of energy and achieved fruitful results. In this paper, based on the previous research results, we consider the generalization of premium income and claim process synthetically, and construct two nonlinear risk models of premium income, which make the model more close to insurance practice. By using the knowledge of complex analysis, stochastic process and risk theory, this paper studies the calculation method of the expected discounted penalty function of these two kinds of models. The main contents of this paper are as follows: the first chapter introduces the classical risk model and its characteristics. Secondly, combined with the main research content of this paper, we briefly review the current research situation at home and abroad, and finally introduce the main research content of this paper. In the second chapter, some conventions are given first, and then some relevant knowledge and tools are given according to the needs of the theoretical research process in this paper. The third chapter extends the premium income process from the linear growth in the classical risk model to the nonlinear Poisson process, and considers that there should be a certain dependence between the claim interval and the amount of claim in the process of settlement. In this paper, an update risk model of Poisson premium income is constructed, in which the premium income is Poisson, and the dependence between claim interval and claim amount satisfies the dependency proposed in Boudreault et alo. (2006). In addition, this chapter discusses the calculation method of the Gerber-Shiu function under the model, and successfully deduces the exact expression of the generating function, and obtains the display expression of the defective update equation satisfied by the generating function. In Chapter 4, we extend the premium income process to the dependent renewal risk model of the compound Poisson process based on the research in Chapter 3. The dependent relation it satisfies is still proposed in Boudreault et al. (2006). In this chapter, by considering the relationship between the interval between the first claim and the arrival time of the first premium income, the expression of the Laplace transform of the Gerber-Shiu function in this dependent case is derived.
【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
【参考文献】
相关期刊论文 前2条
1 ;Ruin Probabilities in the Risk Process with Random Income[J];Acta Mathematicae Applicatae Sinica;2008年02期
2 ;A Ruin Model with Random Income and Dependence between Claim Sizes and Claim Intervals[J];Acta Mathematicae Applicatae Sinica(English Series);2010年04期
相关博士学位论文 前1条
1 张志民;几类风险模型下的Gerber-Shiu分析[D];重庆大学;2010年
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