相位索赔间隔在两种保费率下关于绝对破产的Gerber-Shiu函数  

The Gerber-Shiu discounted penalty function of absolute ruin for two rates with phase-type interclaim times

作　　者：文二园 王秀莲[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《华中师范大学学报（自然科学版）》2018年第1期14-18,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11401436);天津市教委科研项目(043135202JW1714)

摘　　要：在经典风险模型的基础上,在时间间隔为相位分布的情况下研究了有两种保费率的绝对破产风险模型的Gerber-Shiu函数,获得了相应的积分-微分方程,并利用差分的方法获得了初始资金为正和为负两种情况下罚金函数拉普拉斯变换的表达式.On the basis of the classical risk model, this paper considers the Gerber-Shiu discounted penalty function of absolute ruin risk process with two rates, in which the in- ter-claim times have a phase-type distribution. The integro-differential equation for the related rates are obtained. The Laplace transforms of the Gerber-Shiu function with the initial surplus below and above zero are derived by the divided differences of matrix functions.

关 键 词：相位分布 GERBER-SHIU函数 绝对破产 拉普拉斯变换 

分 类 号：O211[理学—概率论与数理统计]