常利率下有阈红利边界的复合Poisson风险模型  

The compound Poisson risk model with a threshold strategy under constant interest

作　　者：贺飞跃[1,2] 刘向增[1] 贺兴时[2] 赵文芝[2] 李志华[1] 

机构地区：[1]西北工业大学理学院,陕西西安710129 [2]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2011年第4期530-535,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(10926197);陕西省专项基金资助项目(2010JK563;2010JK561)

摘　　要：考虑了常利率下有阈红利边界的复合Poisson风险模型,给出了罚金折现期望函数满足的积分-微分方程及带干扰的情况下罚金折现函数所满足的积分-微分方程.利用全概率公式得到了相应积分-微分方程的解、破产概率及破产前瞬时盈余和破产赤字的联合分布的具体表达式.该模型有利于降低公司最终破产的概率.In this paper,it is considered that the expected discounted penalty function for compound Poisson risk process with a threshold strategy under constant interest.Firstly the integro-differential equations and the explicit solution to the integro-differential equations are derived.Secondly the expressions for the ruin probability and the joint distribution of the surplus immediately before ruin and the deficit at ruin are given.Finally it is obtained that the integro-differential equations satisfied by the expected discounted penalty function when the risk process perturbed by diffusion.

关 键 词：罚金折现期望函数 破产概率 积分-微分方程 破产赤字 破产前瞬时盈余 

分 类 号：O211.9[理学—概率论与数理统计]