时刻变换风险模型中的Gerber-Shiu函数  

On the Expected Discounted Penalty Function for the Compound Poisson Risk Model with Time-changing

作　　者：陈旭[1] 欧辉[1] 

机构地区：[1]湖南师范大学数学与计算机学院,长沙410081

出　　处：《应用数学学报》2015年第3期559-567,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11401204;11171101)

摘　　要：本文讨论时刻变换的复合泊松风险模型中的Gerber-Shiu函数,首先给出了Gerber-Shiu函数满足的积微分方程,接着引入Laplace变换的对偶变换Elzaki变换,得到了Gerber-Shiu函数的Elzaki变换的具体形式,最后用一个数值例子验证了用Elzaki逆变换求Gerber-Shiu函数的方法并分析了时刻变换对破产概率的影响.This paper considers the expected discounted penalty function for the com- pound Poisson risk model with time-changing. Integro-differential equation is derived. The Elzaki transform of the expected dscounted penalty function is obtained from the integro- differential equation. Finally, two numerical examples are provided to illustrate the impact of the time-changing on the ruin probability and Gerber-Shiu function.

关 键 词：GERBER-SHIU函数 积微分方程 Elzaki变换 LAPLACE变换 破产概率 

分 类 号：O212.7[理学—概率论与数理统计]