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 :山西师范大学数学与计算机科学学院,临汾;

关键词: 时间间隔为相位分布常利率积分方程微分方程VolterraPhase-Type Inter-Claim Times Constant Integral Function Differential Equation Volterra

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。

Abstract: 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.

文章引用: 肖菊霞 (2014) 带常利率的时间间隔为相位的Gerber-Shiu折现罚金函数。 理论数学, 4, 144-150. doi: 10.12677/PM.2014.44022

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