随机保费下带红利的期望贴现惩罚函数  

Expected Discounted Penalty Functions with Dividend under Random Premiun Income

作　　者：刘再明[1] 李曼曼[1] 张炜[1] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410075

出　　处：《系统工程》2008年第7期52-58,共7页Systems Engineering

基　　金：国家自然科学基金资助项目(10371133);中南大学研究生学位论文创新项目

摘　　要：利用Gerber-Shiu期望贴现惩罚函数统一研究了在保费随机到达和红利边界下的破产问题,推广了Albrecher、Kainhofer(2002)和Bao Zhen-hua(2006)中的结论。首先本文考虑了索赔到达间隔服从普通概率分布时的期望贴现惩罚函数,并得到无红利边界时的极限解;再将红利边界固定为常数,考虑了平稳更新过程和PH更新过程中的结果。最后本文将结论应用于破产概率、破产前盈余的概率分布及破产前盈余过程到达红利边界的概率等实例,并进行了数值实现。The ruin problem is studied unitedly by means of Gerber-Shiu expected discounted penalty function, with the random premium arrival and nonlinear dividend barrier, which generalizes the conclusions of Albrecher and Kainhofer （2002） and Bao Zhen-hua （2006）. Firstly, the paper studies the function under general interclaim arrival time, and the limiting solution is given with no dividend barrier. Moreover, the solution to expected discounted penalty functions are obtained with the stable and the PH renewal process, under the constant dividend barrier. Then the solutions are applied to the practice examples as ruin probability, probability function of the surplus before ruin and the probability of surplus arriving at the barrier before ruin, the numerical illustration is also given.

关 键 词：破产时赤字 破产前瞬时盈余 贴现惩罚函数 随机保费 非线性红利边界 PH分布 

分 类 号：F069[经济管理—政治经济学] O211[理学—概率论与数理统计]