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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报

• • 上一篇    下一篇

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

许  灏,   魏芝雅,   彭旭辉   

  1. 湖南师范大学数学与统计学院，长沙 410081
  • 出版日期:2022-12-15 发布日期:2022-12-15
  • 通讯作者: 彭旭辉 E-mail: xhpeng@hunnu.edu.cn
  • 基金资助:
    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).

Research on Double Compound Poisson-Geometric Processes Insurance Risk Model with Stochastic Portfolios

XU Hao,   WEI Zhiya,   PENG Xuhui   

  1. School of Mathematics and Statistics, Hunan Normal University, Changsha 410081
  • Online:2022-12-15 Published:2022-12-15
  • Contact: X. Peng. E-mail address: xhpeng@hunnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (12071123); the Science and Technology Innovation Program of Hunan Province (2022RC1189); the Scientific Research Project of Hunan Province Education Department (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。

关键词: 破产概率, 鞅, Poisson-Geometric过程, 调节系数, 微积分方程

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.

Key words: ruin probability, martingale, Poisson-Geometric process, adjustment coefficient, integral equation

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