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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (11): 27-34, 52.doi: 10.6040/j.issn.1671-9352.0.2022.370

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二维离散时间风险模型的破产概率

徐诚浩(),王开永*()   

  1. 苏州科技大学数学科学学院, 江苏 苏州 215009
  • 收稿日期:2022-07-08 出版日期:2023-11-20 发布日期:2023-11-07
  • 通讯作者: 王开永 E-mail:534759246@qq.com;beewky@vip.163.com
  • 作者简介:徐诚浩(1997—), 男, 硕士研究生, 研究方向为保险精算. E-mail: 534759246@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11971343);教育部人文社科资助项目(18YJC910004);江苏省“333高层次人才培养工程”资助项目

The ruin probability of a two-dimensional discrete-time risk model

Chenghao XU(),Kaiyong WANG*()   

  1. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
  • Received:2022-07-08 Online:2023-11-20 Published:2023-11-07
  • Contact: Kaiyong WANG E-mail:534759246@qq.com;beewky@vip.163.com

摘要:

讨论二维离散时间风险模型, 在此模型中, 保险公司开展2种业务, 每种业务可以进行无风险和有风险的投资, 即风险模型具有保险风险和金融风险。重点讨论2种业务的保险风险之间存在Sarmanov联合分布、金融风险之间可以任意相依的情形, 在保险风险具有重尾的情况下, 给出风险模型有限时破产概率的渐近估计。同时, 进行数值模拟验证所得理论结果的精确性。

关键词: 二维离散时间风险模型, Sarmanov联合分布, 渐近估计, 有限时破产概率

Abstract:

A two-dimensional discrete-time risk model is considered, in which the insurance company operates two kinds of businesses and each business can put their capital into risk-free and risky portfolio. Then the risk model has insurance and financial risks. Under the assumptions that there exists a Sarmanov joint distribution between two kinds of insurance risks and there are no restrictions on the dependence structure of two kinds of financial risks, asymptotic estimates for the finite-time ruin probabilities are obtained when the distributions of insurance risks are heavy-tailed. At the same time, numerical simulation has been carried to verify the accuracy of the results.

Key words: two-dimensional discrete-time risk model, Sarmanov joint distribution, asymptotic estimate, finite-time ruin probability

中图分类号: 

  • O211.4

图1

当θ=0.2, 0.5, 0.8, x=700, n=5时破产概率渐近值的精确性"

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