带线性红利和干扰的复合Poisson-Geometric风险模型的破产问题  

Ruin Problem in a Compound Poisson-Geometric Risk Model with Linear Dividend and Interference

作　　者：侯致武[1] 乔克林[2] 高磊 HOU Zhiwu;QIAO Kelin;GAO Lei(School of Data Science and Engineering,Xi’an Innovation College of Yan’an University,Xi’an 710100,China;School of Mathematics and Computer Science,Yan’an University,Yan’an 716000,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,陕西西安710100 [2]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《贵州大学学报（自然科学版）》2024年第6期8-13,共6页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金资助项目(31600299);陕西省教育科学规划资助项目(SGH22Y1746,SGH23Y2953)。

摘　　要：考虑了常利力环境下,包含线性红利、随机干扰和随机保费的复合P-G风险模型。通过应用全期望公式,推导出该模型的Gerber-Shiu函数及破产概率的更新方程。在不考虑分红且保费额和索赔额均服从指数分布时,进一步得到了破产概率所满足的具体微分方程,并求解得到了其解析表达式。通过数值实验,系统分析了多个关键因素对破产概率的具体影响,所得结论与保险公司的实际经营情况相吻合。A compound P-G risk model considering linear dividends,random disturbances,and random premiums in a constant profit environment is considered.By applying the full expectation formula,the update equation for the Gerber-Shiu function and the update equation for the ruin probability of the model are derived.When dividends are not considered and both premium and claim amounts follow an exponential distribution,the specific differential equation satisfied by the ruin probability is further obtained,and its analytical expression is solved.Through numerical experiments,the specific impact of multiple key factors on bankruptcy probability was systematically analyzed.The conclusions drawn align with the real operational circumstances encountered by insurance companies.

关 键 词：复合POISSON-GEOMETRIC过程 线性红利 GERBER-SHIU函数 破产概率 

分 类 号：O211.6[理学—概率论与数理统计]