常利率下分红双复合Poisson风险模型的期望折现罚金函数  

On Expected Discounted Penalty Function for Double Compound Poisson Risk Model with Constant Interest and Dividends

作　　者：王贵红 赵金娥[2] 何树红[3] 

机构地区：[1]玉溪农业职业技术学院计科系,云南玉溪653106 [2]红河学院数学学院,云南蒙自661100 [3]云南大学数学与统计学院,昆明650091

出　　处：《西南师范大学学报（自然科学版）》2016年第1期94-99,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11301160);云南省科技厅自然科学研究基金项目(2013FZ116);云南省教育厅科研基金项目(2013C014);红河学院科研基金项目(XJ15SX06)

摘　　要：对常利率和常数红利边界策略下的双复合Poisson风险模型进行研究,其中保费收入不再是时间的线性函数,而是一个与理赔过程独立的复合Poisson过程.得到了期望折现罚金函数、破产时的Laplace变换、破产时赤字的期望折现函数以及破产概率满足的积分—微分方程,并借助confluent hypergeometric函数给出指数保费和指数索赔下破产概率的具体表达式.In this paper,a double compound Poisson risk model has been considered.In contrast with the classical risk model where the premium process is a linear function of time,the aggregate premium process is a compound Poisson process,and it is also independent of the claim process.Moreover,there are a constant interest and a constant dividend barrier strategy in this model.The integro-differential equations for the expected discounted penalty function,the Laplace transform of the time of ruin,the discounted expectation of the deficit at ruin and the ruin probability are derived.Meanwhile,the explicit expression for the ruin probability is given in terms of the confluent hypergeometric functions when the individual stochastic premium amount and claim amount are exponentially distributed.

关 键 词：红利 常利率 期望折现罚金函数 破产概率 合流超几何函数 

分 类 号：O211.6[理学—概率论与数理统计]