一类带干扰的复合Poisson-Geometric风险模型的生存概率  

Survival Probability of 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,陕西西安710100 [2]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《沈阳大学学报（自然科学版）》2022年第1期71-76,共6页Journal of Shenyang University：Natural Science

基　　金：国家自然科学基金资助项目(31600299);陕西省自然科学基础研究计划项目(2017JQ3020);陕西省教育科学规划课题(SGH18H466)。

摘　　要：研究了一类常利力下带干扰且保费随机的复合Poisson-Geometric风险模型的生存概率。利用盈余过程的强马氏性和ItÔ公式,给出了作为保险公司生存概率的积分微分方程。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。通过数值实验分析了保险公司的生存概率随利率、初始资本、保费、索赔额等的变化情况及对保险公司稳定运营的影响,验证了结果的合理性。The survival probability of a compound Poisson-Geometric risk model with interference and random premium under constant interest was studied. By using the strong Markov property of the surplus process and ItÔ formula, an integral-differential equation for the survival probability of an insurance company was given.When both the premium and the claim amount obey exponential distribution, the differential equation and the analytical solution under special cases were further derived. The numerical experiments were carried out to analyze the variation of the survival probability of an insurance company with interest rate, initial capital, premium and claim amount, and the influence on the stable operation of the insurance company.The rationality of the results was verified.

关 键 词：常利力 复合Poisson-Geometric风险模型 生存概率 积分微分方程 ItÔ公式 

分 类 号：O211.6[理学—概率论与数理统计]