对股东和投保人均分红的带干扰的复合泊松风险模型(英文)  

The Compound Poisson Risk Model Perturbed by Diffusion with Double-Threshold Dividend Barriers to Shareholders and Policyholders

作　　者：周杰明[1] 欧辉[1] 莫晓云[1,2] 杨向群[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,高性能计算与随机信息处理省部共建重点实验室,中国长沙410081 [2]湖南财政经济学院基础课部,中国长沙410205

出　　处：《湖南师范大学自然科学学报》2012年第6期1-13,共13页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(11171101);湖南师范大学青年基金资助项目(71001);湖南省研究生科研创新资助项目(CX2011B197)

摘　　要：用一个带干扰的复合泊松风险模型去刻画一个保险公司的盈余过程,考虑了具有2个不同水平的阈分红门槛策略的分红问题,假设保险公司的分红率是一个依赖当前盈余水平的阶梯函数,得到了破产之前的期望折现分红总量所满足的3个积分-微分方程,并给出了显示解;同时还得到了该模型下的Gerber-Shiu期望折罚函数的精确表达式.In the absence of dividends,the surplus of an insurance company is modelled by a compound Poisson process perturbed by diffusion.Double-threshold dividend strategy is addressed here.Under the assumption that the dividend rate is a step function depending on the current surplus level,three integro-differential equations for the expected discounted dividend payments prior to ruin are derived,and their closed-form solutions are given.Finally,the explicit formulas for the Gerber-Shiu expected discounted penalty function are also obtained.

关 键 词：复合泊松风险过程 扩散 布朗运动 阈分红策略 Gerber-Shiu期望折罚函数 

分 类 号：F224[经济管理—国民经济] F830.91