一类变保费率风险模型的Gerber-Shiu惩罚函数  

GERBER-SHIU DISCOUNTED PENALTY FUNCTION FOR RISK MODEL WITH PREMIUM RATE DEPENDING ON TIME

作　　者：王刈禾[1] 胡亦钧[2] 

机构地区：[1]襄樊学院数学系,湖北襄樊441003 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2010年第6期1114-1116,共3页Journal of Mathematics

基　　金：国家自然基金资助项目(10671149)

摘　　要：本文考虑变保费风险模型,假设保费率是随时间变化的,研究了其Gerber-Shiu惩罚函数.通过无穷小方法给出Gerber-Shiu惩罚函数所满足的积分-微分方程;在指数索赔下,给出其破产时赤字的数学期望及破产时的拉普拉斯变换.In this article, we consider the risk model in which the premium rate is assumed to depend upon time. Under this condition, we consider the Gerber-Shiu discounted penalty function for this risk model. By using ＂diffential argument＂, an integro-differential equation for Gerber-Shiu discounted penalty function is given, and is also solved in some special cases.

关 键 词：保费率 破产时 Gerber-Shiu惩罚函数 赤字 

分 类 号：O211.6[理学—概率论与数理统计]