| 具有随机投资组合的双复合 Poisson-Geometric 过程保险风险模型的研究 |
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| 引用本文： | 许 灏,魏芝雅,彭旭辉.具有随机投资组合的双复合 Poisson-Geometric 过程保险风险模型的研究[J].工程数学学报,2022,39(6):875-885. |
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| 作者姓名： | 许 灏 魏芝雅 彭旭辉 |
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| 作者单位： | 湖南师范大学数学与统计学院，长沙 410081 |
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| 基金项目： | 国家自然科学基金(12071123)；湖南省科技创新计划(2022RC1189)；湖南省教育厅重点项目(20A329). |
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| 摘 要： | 研究了一个双复合Poisson-Geometric过程保险风险模型，其中保费和索赔的发生均服从复合泊松几何过程。通过鞅方法和停时的技巧，得到了关于破产概率的Lundberger不等式，调节系数方程和破产概率的表达式。生存概率可以作为衡量支付能力的指标，文章得到了无限和有限时间生存概率的微积分方程。
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| 关 键 词： | 破产概率 鞅 Poisson-Geometric过程 调节系数 微积分方程 |
Research on Double Compound Poisson-Geometric Processes Insurance Risk Model with Stochastic Portfolios |
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| XU Hao,WEI Zhiya,PENG Xuhui.Research on Double Compound Poisson-Geometric Processes Insurance Risk Model with Stochastic Portfolios[J].Chinese Journal of Engineering Mathematics,2022,39(6):875-885. |
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| Authors: | XU Hao WEI Zhiya PENG Xuhui |
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| Affiliation: | School of Mathematics and Statistics, Hunan Normal University, Changsha 410081 |
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| Abstract: | A double compound Poisson-Geometric processes insurance risk model is investigated, in which the arrivals of premiums and claims are compound Poisson-Geometric processes. Through the martingale method and stopping time technique, we get the Lundberg inequality, adjustment coefficient equation and formula about the ruin probability. Also obtained are the integral differential equations for survival probabilities of infinite intervals and finite intervals, respectively, which can be regarded as indices to measure the payment ability. |
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| Keywords: | ruin probability martingale Poisson-Geometric process adjustment coefficient integral equation |
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