一类具有相依结构的连续时间更新过程的期望罚金函数

发布时间：2018-02-25 04:03

本文关键词： 具有相依结构的复合泊松风险模型 Gerber-Shiu罚金函数拉普拉斯变换积分方程　出处：《辽宁师范大学》2014年硕士论文　论文类型：学位论文

【摘要】：经典的复合泊松风险模型是精算文献中研究得最深入的连续时间更新风险过程,近些年来,许多精算学者从不同的方面把经典复合泊松风险模型进行了推广,得到了许多有价值的结论。在经典的复合泊松风险模型的基础上,本文研究两种相依结构模型下关于Gerber-Shiu函数的积分方程,并且对Gerber-Shiu函数的几个数学特征及一些相关破产量的贴现密度做了深入研究。本论文共分为四章：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,然后对经典复合泊松风险模型及Gerber-Shiu函数做了综合性的回顾,最后介绍了本文的主要工作。第二章本章研究关于Gerber-Shiu函数的积分方程mδ(u)和mδ(u)的分析,首先定义一个新的变量,即第n次索赔之后的即时盈余Rn,得到一个关于Gerber-Shiu函数的积分方程mδ(u),然后对积分方程mδ(u)的一些数学特征进行分析,得到mδ(u)另一种形式解析表达式。第三章本章研究一些相关破产量的贴现密度函数,在上一章的基础上首先给出一个恰当的罚金函数,然后派生出一些相关破产量的贴现联合密度和贴现边际密度的基本结构。第四章本章研究具有相依结构的延迟更新风险过程的Gerber-Shiu函数,得到一个关于Gerber-Shiu函数的积分方程md,δ(u),并且对积分方程md,δ(u)做了分析。
[Abstract]:The classical compound Poisson risk model is the most deeply studied continuous time updating risk process in the actuarial literature . In recent years , many researchers have extended the classical composite Poisson risk model from different aspects . Based on the classical compound Poisson risk model , this paper studies the integral equation of Gerber - Shiu function under the two dependent structure models , and makes a further study on some mathematical features of Gerber - Shiu function and the discount density of some related broken yields . This thesis is divided into four chapters : In chapter 1 , this chapter briefly introduces the theory of risk theory and its core content bankruptcy theory , then reviews the classical composite Poisson risk model and Gerber - Shiu function , and finally introduces the main work of this paper . In chapter 2 , we study the integral equation m 未 ( u ) and m 未 ( u ) of Gerber - Shiu function , first define a new variable , i.e . the instantaneous surplus Rn after the nth claim , get an integral equation m 未 ( u ) about Gerber - Shiu function , then analyze some mathematical features of the integral equation m 未 ( u ) to obtain another form resolution expression of m 未 ( u ) . In chapter 3 , we study the discount density function of some related broken yields . Based on the previous chapter , a proper penalty function is given first , then the basic structure of the discount joint density and discount margin density of some related broken yields is derived . In chapter 4 , we study the Gerber - Shiu function with dependency structure to update the risk process , get an integral equation md , 未 ( u ) for Gerber - Shiu function , and analyze the integral equation md , 未 ( u ) .

【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840.4;O211.67

【相似文献】