一类具有一般保费收入的离散时间风险模型  

A class of discrete time risk model with general premium income

作　　者：包振华[1] 刘叶[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2015年第2期150-155,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省高等学校优秀人才支持计划(LR2014031)

摘　　要：研究一类具有一般保费收入的离散时间更新风险模型,模型中假设索赔的间隔等待时间服从离散的Km分布.利用鞅技巧得到了模型的Lundberg基本方程并讨论了该方程在单位圆内根的情况.利用Lundberg基本方程的根研究了Gerber-Shiu期望贴现惩罚函数的概率生成函数,并且获得了初值为零时惩罚函数的分析表达式.作为推论,得到了破产前盈余及破产发生时赤字的贴现密度等相关破产量的显性表达.给出了破产发生时赤字的贴现密度的概率生成函数的具体计算公式.In this paper we deal with discrete time risk model with general premium income ,in which the inter‐claim times follow discrete Km distributions .By using the martingale method ,we first get the Lundberg’s fundamental equation and the roots in the unit circle are also analyzed . T hen the probability generating function satisfied by the Gerber‐Shiu expected discounted penalty function is derived by using the zeros of Lundberg’s equation ,and the expression for the penalty function with zero initial is also obtained .As corollaries ,we get the expressions for some ruin quantities such as the discounted densities for surplus before ruin and deficit at ruin .Finally ,the explicit formula of the probability generating function satisfied by the discounted density of deficit is given .

关 键 词：离散的 Km分布 概率生成函数 Lundberg基本方程 Gerber-Shiu期望贴现惩罚函数 

分 类 号：O211.67[理学—概率论与数理统计]