一类带干扰的复合Poisson-Geometric风险模型的预警区问题  

Duration of Negative Surplus for a Compound Poisson-Geometric Risk Model with Disturbance

作　　者：侯致武[1] 高磊 HOU Zhiwu;GAO Lei(School of Data Science and Engineering,Xi’an Innovation College of Yan’an University,Xi’an 710100,China;School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,China)

机构地区：[1]延安大学西安创新学院数据科学与工程学院,西安710100 [2]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《重庆理工大学学报（自然科学）》2020年第6期232-238,共7页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(31600299);陕西省教育厅专项科学研究计划项目(18JK1216,18JK1217)。

摘　　要：研究一类常利率下带干扰且保费随机的复合Poisson-Geometric风险模型的预警区问题,利用全期望公式和It公式,得到了第一预警区的条件矩母函数所满足的积分-微分方程。当保费额和索赔额均服从指数分布时,进一步推出其所满足的微分方程及特殊情形下的解析解,通过数值算例分析了盈余、保费额、索赔额等对第一预警区的条件矩母函数的影响。The duration of negative surplus of a compound Poisson-Geometric risk model with constant interest,disturbance and random premium was studied.By the total expectation formula and Ito formula,an integral-differential equation of a conditional moment generating function of the first duration of negative surplus was obtained.Finally,the differential equation and the analytical solution to special circumstances was introduced when the premium and the claim was exponential distributions.The effects of surplus,premium and claim amount on the conditional moment generating function of the first duration of negative surplus were analyzed by a numerical example.

关 键 词：常利率 复合Poisson-Geometric风险模型 预警区 条件矩母函数 

分 类 号：O211.6[理学—概率论与数理统计]