带分红和不定期观察的保险公司的建模研究（英文）  

A Model about Insurer with Dividend and Irregularly Checking Surplus

作　　者：金芳[1] 莫晓云[2,3] 杨向群[4] 

机构地区：[1]湖南城市学院数学与计算科学学院,益阳413000 [2]湖南财政经济学院数学与统计学院,长沙410205 [3]高性能计算与随机信息处理教育部重点实验室 [4]湖南文理学院数学与计算科学学院,湖南415000

出　　处：《应用概率统计》2017年第2期125-138,共14页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11631132;11626094);Scientic Research Foundation of Hunan Provincial Department(Grant Nos.16C0296;15A032)

摘　　要：文中用不可约的齐次离散时间马氏链来调控保险公司的观察时间间隔,在此基础上引入门槛分红因素,给出带分红的马氏观察模型的数学定义和实际意义和解释.在带分红的马氏观察模型里,首先得到了破产前的折现分红总量所满足的一系列方程,然后计算出了破产前的折现分红总量的精确表达式并给出证明.最后,通过数值模型和与带分红的复合二项风险模型的对比分析,总结出一些带分红的马氏观察模型的性质特点.A Markov observation model with dividend is defined and the interpretation of the practical significance is given. We try to use an irreducible and homogeneous discrete-time Markov chain to modulate the inter-observation times and embed a dividend strategy. In the Markov observation model with dividend, a system of liner equations for the expected discounted value of dividends until ruin time is derived. Moreover, an explicit expression is obtained and proved. Finally, some interesting properties are illustrated by numerical analysis and by comparing with the complete compound binomial model with dividend.

关 键 词：马氏观察 马氏链 常数分红边界 折现值 破产时 

分 类 号：O211.62[理学—概率论与数理统计]