| 黄鸿君1
，覃利华2*.带混合保费和投资复合Poisson-Geometric风险模型
的生存概率[J].海南师范大学学报自科版,2022,35(3):260-267 |
| 带混合保费和投资复合Poisson-Geometric风险模型
的生存概率 |
| The Survival Probability of an Poisson-Geometric Risk Model withMixed Premium and Investment |
| |
| DOI：10.12051/j.issn.1674-4942.2022.03.004 |
| 中文关键词: 复合Poisson-Geometric过程 生存概率 积分微分方程 混合保费 |
| 英文关键词: compound Poisson-Geometric process survival probability integral-differential equations mixed premium |
| 基金项目: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经费资助项目
（2021YB054） |
|
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| 中文摘要: |
| 在考虑到保费收入和通货膨胀等随机因素的干扰以及保险公司将多余资本用于投资
来提高其赔付能力的基础上，本文对经典风险模型进行了推广。首先，建立了混合保费收取下带
投资和扰动的双复合Poisson-Geometric 过程的双险种风险模型，随机保费收入服从复合Poisson过
程，理赔过程服从复合Poisson-Geometric过程；其次，应用全期望公式，推导了该模型生存概率的积
分微分方程；最后，当保费、理赔过程服从特定指数分布时，得到其满足的微分方程。 |
| 英文摘要: |
| Taking into account the disturbance of random factors such as premium income and inflation, as well as the ex⁃
cess capital invested by insurance companies to improve their payability, the classical risk model is extended in this paper.
Firstly, a double risk model with investment and perturbation is established under the mixed premium collection. The sto⁃
chastic premium income follows the compound Poisson process, and the claims process follows the compound Poisson-Geo⁃
metric process. Secondly, the integral differential equation of the survival probability of the model is derived by using the to⁃
tal expectation formula. Finally, when the premium and claim process obey a specific exponential distribution, the differen⁃
tial equation satisfied is obtained. |
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