常利率下保费随机收取风险模型分红问题的研究  

Dividend Payments under the Risk Model with Stochastic Premium and Constant Interest

作　　者：赵金娥 王贵红 曾黎 李明 ZHAO Jin-e;WANG Guihong;ZENG Li;LI Ming(School of Mathematics and Statistics,Honghe University,Mengzi,661199,China)

机构地区：[1]红河学院数学与统计学院,蒙自661199

出　　处：《应用概率统计》2023年第5期701-710,共10页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:12161033、12361085);云南省科技厅高校联合基金面上项目(批准号:2017FH001-015、202101BA070001-046);云南省教育厅科研基金资助项目(批准号:2021J0548、2022J0896);红河学院博士专项(批准号:XJ22B18)资助.

摘　　要：对常利率下保费收入为复合Poisson过程风险模型的分红问题进行研究,得到了直至破产时累积分红现值的期望、n阶矩及矩母函数满足的积分–微分方程及指数保费和指数索赔下的具体表达式.并给出数值算例,分析了初始资本u、红利界限b及投资利率r对累积分红期望现值的影响.In this paper,we consider a risk model where the aggregate premium process is a compound Poisson process.Moreover,there are a constant interest and a constant dividend barrier strategy in this model.The integro-differential equations for the expectation and the nth moment and the moment generating function of the cumulative discounted dividend payments until ruin are obtained.Meanwhile,the explicit expressions for the expectation and the nth moment and the moment generating function of the cumulative dividend payments until ruin are given when the individual stochastic premium amount and claim amount are exponentially distributed.Finally,numerical example is also given to illustrate the effect of the related parameters on the expected value of the cumulative discounted dividend payments until ruin.

关 键 词：常利率 累积分红现值 合流超几何函数 

分 类 号：O211.6[理学—概率论与数理统计]