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

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.