带投资和分红策略下复合Poisson-Geometric风险模型的研究  

RESEARCH ON COMPOUND POISSON-GEOMETRIC RISK MODEL WITH INVESTMENT AND DIVIDEND STRATEGIES

作　　者：覃利华 李越洋 QIN Lihua;LI Yueyang(School of Mathematics and Computer Science,Guangxi Minzu Normal University,Chongzuo,Guangxi 532200,China)

机构地区：[1]广西民族师范学院数学与计算机科学学院,广西崇左532200

出　　处：《井冈山大学学报（自然科学版）》2024年第5期9-16,共8页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11801105);广西教育科学“十四五”规划2023年度专项项目(2023ZJY846);广西高校中青年教师科研基础能力提升项目(2021KY0767);广西民族师范学院科研项目(2022YB019)。

摘　　要：考虑投资和分红策略下,建立带有混合收费及索赔计数服从复合Poisson-Geometric过程的风险模型。运用全期望公式与积分变换公式,研究该模型红利付款现值期望函数满足的微积分方程和特定指数分布下满足的微分方程及解析解,通过数值模拟分析了固定保费率、初始资本、投资资产、索赔强度和红利边界对红利付款现值期望函数的影响,并分析其经济意义。Considering investment and dividend strategies,a risk model with mixed charges and claims following a compound Poisson-Geometric process was established.By using the full expectation formula and integral transformation formula,the micro-integral equation satisfied by the dividend payment expectation function of this model and the differential equation and analytic solution satisfied under specific exponential distribution were studied.The effects of fixed premium rate,initial capital,investment assets,claim intensity and dividend boundary on the dividend payment expectation function were analyzed by numerical simulation,and their economic significance was also analyzed.

关 键 词：复合POISSON-GEOMETRIC过程 红利付款现值期望函数 分红策略 投资策略 积分微分方程 

分 类 号：O211.5[理学—概率论与数理统计]