带常利率的时间间隔为相位的Gerber-Shiu折现罚金函数  

The Gerber-Shiu Discounted Penalty Function for the Risk Model with Phase-Type Inter Claim Times

作　　者：肖菊霞[1] 

机构地区：[1]山西师范大学数学与计算机科学学院,临汾

出　　处：《理论数学》2014年第4期144-150,共7页Pure Mathematics

摘　　要：相位分布的研究在研究正半轴的其他分布中起着重要作用。考虑带常利率的时间间隔为相位分布的更新风险模型。首先推导出Gerber-Shiu期望折现罚金函数满足的积分微分方程,然后经过一系列的推导过程得到Volterra形式的矩阵积分方程,从而得到Gerber-Shiu期望折现罚金函数的一种解法。Research in the phase-type distribution has an important influence for the research of other dis-tributions on the positive real axis. It considers the risk model with the phase-type inter-claim times and for constant interest, it first derives the integral-differential equation satisfied by the Gerber-Shiu discounted penalty function. Then through a series of deriving, it obtains the volterra integral equation in a form of matrix. It gets a method of solving the Gerber-Shiu expected penalty function.

关 键 词：时间间隔为相位分布 常利率 积分方程 微分方程 VOLTERRA 

分 类 号：F2[经济管理—国民经济]