基于广义FGM模型下复合泊松过程的保费定价研究
发布时间：2019-03-20 11:03
【摘要】：一直以来,保费价格都是保险理论和实践中研究的核心问题.保险公司的业务可以用一个输入输出系统来描述,在这个系统中,盈余由征收的保费和赚取的利息以及投资收益而增加,由理赔和成本的支出而减少.保费定价过低会使保险公司陷入经营困境甚至会导致破产,定价过高会使保险公司降低市场竞争力且会增加被保险人负担,因此保费定价对保险公司来说是非常重要的精算问题.保费的厘定就是求出一个最小保费,它不仅可以应付理赔,而且还使得保单组合的盈余足够快增长.保费的厘定,对保险公司的生死存亡至关重要,因此,合理的风险定价模式,一直备受保险工作者和理论界广泛关注. 本文首先从保费定价的基本理论入手,考虑了索赔额与等待时间是一组具有广义FGM相依结构的序列,在复合泊松过程模型的假设下,对保费定价进行了深入的探索和研究,相对于索赔额与等待时间独立的情形更加符合实际.在确定复合泊松过程下的广义FGM Copula的分布函数后,求得出其概率密度函数,通过Laplace变换、Laplace逆变换等方法求出了索赔额的矩母函数的表达式,并对比了索赔额与等待时间独立情形的矩母函数. 随后文章进一步讨论了矩母函数的高阶导数计算方法,给出了其Esscher定价泛函的表达式,利用Matlab软件对Esscher定价泛函与参数h之间的关系进行了数值模拟,并在零利息力和非零利息力下分别讨论了净保费的表达式. 最后,文章对全文的研究结果做了总结,并介绍了作者下一步的工作计划.
[Abstract]:Premium price has always been the core issue of insurance theory and practice. The insurance company's business can be described as an input-output system in which earnings are increased by levied premiums and interest earned as well as investment returns and reduced by expenses for claims and costs. Too low premium pricing will put insurance companies into business difficulties or even lead to bankruptcy. Overpricing will make insurance companies less competitive in the market and increase the insurant's burden. Therefore, premium pricing is a very important actuarial issue for insurance companies. The premium is determined to work out a minimum premium, which not only pays for claims, but also makes the surplus of the policy portfolio grow fast enough. The determination of premium is very important to the life and death of insurance company. Therefore, the reasonable risk pricing model has been paid more and more attention by insurance workers and theorists. First of all, this paper starts with the basic theory of premium pricing, considering that the claim amount and waiting time are a series of generalized FGM dependent structures. Under the assumption of compound Poisson process model, the premium pricing is deeply explored and studied. The situation where the claim amount is independent of the waiting time is more realistic. After determining the distribution function of the generalized FGM Copula under the compound Poisson process, the probability density function is obtained, and the expression of the moment generating function of the claimed amount is obtained by means of Laplace transform and Laplace inverse transformation, etc. The moment generating function of claim amount and waiting time independent case is compared. Then, the calculation method of higher order derivative of moment generating function is discussed, the expression of Esscher pricing functional is given, and the relationship between Esscher pricing function and parameter h is numerically simulated by using Matlab software. The expressions of net premium are discussed under zero interest force and non zero interest force respectively. Finally, the paper summarizes the research results and introduces the author's next work plan.
【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】：F840.31;F224
本文编号：2444157
[Abstract]:Premium price has always been the core issue of insurance theory and practice. The insurance company's business can be described as an input-output system in which earnings are increased by levied premiums and interest earned as well as investment returns and reduced by expenses for claims and costs. Too low premium pricing will put insurance companies into business difficulties or even lead to bankruptcy. Overpricing will make insurance companies less competitive in the market and increase the insurant's burden. Therefore, premium pricing is a very important actuarial issue for insurance companies. The premium is determined to work out a minimum premium, which not only pays for claims, but also makes the surplus of the policy portfolio grow fast enough. The determination of premium is very important to the life and death of insurance company. Therefore, the reasonable risk pricing model has been paid more and more attention by insurance workers and theorists. First of all, this paper starts with the basic theory of premium pricing, considering that the claim amount and waiting time are a series of generalized FGM dependent structures. Under the assumption of compound Poisson process model, the premium pricing is deeply explored and studied. The situation where the claim amount is independent of the waiting time is more realistic. After determining the distribution function of the generalized FGM Copula under the compound Poisson process, the probability density function is obtained, and the expression of the moment generating function of the claimed amount is obtained by means of Laplace transform and Laplace inverse transformation, etc. The moment generating function of claim amount and waiting time independent case is compared. Then, the calculation method of higher order derivative of moment generating function is discussed, the expression of Esscher pricing functional is given, and the relationship between Esscher pricing function and parameter h is numerically simulated by using Matlab software. The expressions of net premium are discussed under zero interest force and non zero interest force respectively. Finally, the paper summarizes the research results and introduces the author's next work plan.
【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】：F840.31;F224
【参考文献】
相关期刊论文 前3条
1 董永权;;FGM Copula的生成与拓展[J];工程数学学报;2008年06期
2 沈银芳;修整保费——一个新的定价模型[J];数学的实践与认识;2005年09期
3 徐付霞;史道济;董永权;;广义FGM Copula的一个判定定理及应用[J];应用数学学报;2007年03期
，本文编号：2444157
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