索赔额服从混合指数分布的一类期望折现罚金函数  

A class of expected discounted penalty function for claim size of mixed exponential distribution

作　　者：邵晶晶 王秀莲[1] 邹华 SHAO Jingjing;WANG Xiulian;ZOU Hua(College of Mathematical Science, Tianjin Normal University, Tianjin 300387, Chin)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2018年第3期5-7,共3页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11401436)

摘　　要：基于经典风险模型,针对指数索赔间隔和混合指数索赔额的情况,研究关于实质破产的期望折现罚金函数.首先,利用全概率公式得到期望折现罚金函数满足的积分微分方程;然后,在索赔额为混合指数分布的情况下推导出期望折现罚金函数满足的微分方程,进而针对常数破产率函数,得到期望折现罚金函数的具体表达式.Based on the classical risk model,the expected discounted penalty function about bankruptcy is studied with exponentially inter-claim times and mixed exponentially claim size. First,the integro-differential equations that satisfy discounted penalty function are obtained by total probability formula. Then,the differential equations for the discount penalty function are obtained when the claim size is mixed exponentially distribution,and for constant bankruptcy rate function,the explicit formula of the discount penalty function is deduced.

关 键 词：混合指数分布 期望折现罚金函数 实质破产 破产率函数 

分 类 号：O211.67[理学—概率论与数理统计]