关于Copula相依风险模型绝对破产问题的研究

发布时间：2018-03-17 20:37

本文选题：绝对破产　切入点：折罚函数　出处：《湖南师范大学》2013年硕士论文　论文类型：学位论文

【摘要】：自从瑞典精算师Filip Lundberg提出复合泊松风险模型之后,许多学者通过放宽关于索赔时间和索赔额分布等的假设,将经典复合泊松风险模型进行了一些列的推广,他们主要是计算最终破产概率,1998年,Gerber-Shiu提出了折罚函数后,风险理论得到了很大的发展.本文考虑了在索赔额与索赔来到时间具有经典FGM Copula相依关系的复合泊松风险模型下的绝对破产问题,给出了此模型下Gerber-Shiu折罚函数的微分积分方程,然后研究了当初始值大于0时绝对破产折罚函数的拉普拉普拉斯变换,并在此变换下得到了更新方程,最后给出了在特殊情况下的绝对破产概率. 本文的第一章主要是介绍风险理论发展史以及相依风险风险模型的研究现状和绝对破产问题研究的一些成果.第二章主要给出了本文所用到相关知识及模型. 本文核心在第三章和第四章.第三章主要研究了绝对破产折罚函数满足的积分微分方程,并且当初始值大于0时,通过拉普拉斯变换得到了绝对破产折罚函数满足的更新方程,并得到了其解析表达式.第四章主要研究了在特殊情况下绝对破产概率的解析表达式.
[Abstract]:Since the Swedish actuary Filip Lundberg put forward the compound Poisson risk model, many scholars have extended the classical compound Poisson risk model by relaxing the assumptions about the claim time and the distribution of claim amount. In 1998, Gerber-Shiu proposed a penalty function. The risk theory has been greatly developed. In this paper, we consider the absolute ruin problem under the compound Poisson risk model with the classical FGM Copula dependence between the claim amount and the claim arrival time, and give the differential integral equation of the Gerber-Shiu folding function in this model. Then we study the Laplacian transformation of the absolute ruin penalty function when the initial value is greater than 0:00, and obtain the renewal equation under this transformation. Finally, the absolute ruin probability in special cases is given. The first chapter mainly introduces the history of risk theory, the current research situation of dependent risk risk model and some achievements of absolute bankruptcy. The second chapter mainly gives the relevant knowledge and model used in this paper. The core of this paper is in Chapter 3 and Chapter 4th. In Chapter 3, we study the integro-differential equation satisfied by the absolute ruin penalty function, and when the initial value is greater than 0:00, By means of Laplace transformation, the renewal equation of absolute ruin penalty function is obtained, and its analytical expression is obtained. Chapter 4th mainly studies the analytical expression of absolute ruin probability in special cases.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F842;O211.63

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