带延迟索赔和随机收入的离散风险模型的Gerber-Shiu分析（英文）  

Gerber-Shiu Analysis for a Discrete Risk Model with Delayed Claims and Random Incomes

作　　者：黄娅[1] 刘娟 周杰明 邓迎春 HUANG Ya;LIU Juan;ZHOU Jie-ming;DENG Ying-chun(School of Business,Hunan Normal University,Changsha 410081;Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education),School of Mathematics and Statistics,Hunan Normal University,Changsha 410081)

机构地区：[1]湖南师范大学商学院,长沙410081 [2]湖南师范大学数学与统计学院,计算与随机数学教育部重点实验室,长沙410081

出　　处：《工程数学学报》2020年第1期89-106,共18页Chinese Journal of Engineering Mathematics

基　　金：The Philosophy and Social Science Fund of Hunan Province(17YBA290);the Scientific Research Fund of Hunan Provincial Department of Education(17K057;17C1001)~~

摘　　要：破产理论是保险数学中的重要问题,它可以为保险公司决策者提供一个非常有用的早期风险预警手段.本文研究了一个带潜在延迟索赔和随机保费收入的复合二项风险模型.利用矩母函数的技巧,得到了Gerber-Shiu期望折罚函数的递推公式.特别地,还得到了贴现因子为1的特殊情形下的Gerber-Shiu期望折罚函数的解析表达式.最后还得到了实际应用中的一些重要的破产特征量,包括破产概率,破产时赤字的密度函数,破产前盈余与破产时赤字的联合密度函数,以及导致破产的索赔密度函数等.Ruin theory is the mainly contents of insurance mathematics,as it can supply a very useful early-warning measure for the risk of the insurance company.In this paper,we study a risk model with potentially delayed claims and random premium incomes within the framework of the compound binomial model.Using the technique of generating functions,we derive a recursive formula for the Gerber-Shiu expected discounted penalty function.Specifically,an explicit formula is obtained for the discount-free case.As applications,we derive some useful insurance quantities,including the ruin probability,the density of the deficit at ruin,the joint density of the surplus immediately before ruin and the deficit at ruin,and the density of the claim causing ruin.

关 键 词：复合二项风险模型 Gerber-Shiu期望折罚函数 延迟索赔 随机保费 递推公式 

分 类 号：O211.67[理学—概率论与数理统计]