考虑一般投资收益和时间相依索赔情形下二维带扰动风险模型的有限时间破产概率渐近估计

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1529-1558.

考虑一般投资收益和时间相依索赔情形下二维带扰动风险模型的有限时间破产概率渐近估计

程铭(),王定成^*()

电子科技大学数学科学学院成都 611731

收稿日期:2021-06-21 修回日期:2022-07-05 出版日期:2023-10-26 发布日期:2023-08-09
通讯作者: 王定成 E-mail:chming@std.uestc.edu.cn;wangdc@uestc.edu.cn
作者简介:程铭，Email: chming@std.uestc.edu.cn
基金资助:
国家自然科学基金(71271042);云南师范大学博士科研启动项目(2020ZB014);云南省基础研究青年项目(202201AU070051)

Asymptotic Finite-Time Ruin Probability for a Bidimensional Perturbed Risk Model with General Investment Returns and Time-Dependent Claim Sizes

Cheng Ming(),Wang Dingcheng^*()

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731

Received:2021-06-21 Revised:2022-07-05 Online:2023-10-26 Published:2023-08-09
Contact: Dingcheng Wang E-mail:chming@std.uestc.edu.cn;wangdc@uestc.edu.cn
Supported by:
NSFC(71271042);Yunnan Normal University(2020ZB014);Yunnan Province Science and Technology Department(202201AU070051)

摘要/Abstract

摘要：

考虑具有一般投资收益过程的二维带扰动保险风险模型, 假定保险公司盈余的投资收益过程由右连左极随机过程刻画, 且两种索赔额与索赔到达时间间隔服从 Sarmanov 相依结构. 当索赔额分布属于正则变化尾分布族时, 得到有限时间破产概率的渐近公式. 当描述投资收益过程的右连左极过程分别取 Lévy 过程, Vasicek 利率模型, Cox-Ingersoll-Ross(CIR) 利率模型, Heston 模型时, 得到相应投资收益情形下破产概率的渐近公式.

关键词: 风险模型, 投资收益, 时间相依, 破产概率

Abstract:

The paper considers a bi-dimensional perturbed insurance risk model with general investment returns. Assume that the investment return is described by a càdlàg process, and two classes of claims and the inter-arrival times follow the Sarmanov dependence structure. When the claim-size distribution has a regularly varying tail, the paper derives the asymptotic formula of the finite-time ruin probability. When the càdlàg process describing investment returns is chosen as the Lévy process, Vasicek interest rate model, Cox-Ingersoll-Ross (CIR) interest rate model, or Heston model, the paper derives the asymptotic estimates for ruin probabilities under the corresponding investment returns.

Key words: Risk model, Investment return, Time-dependence, Ruin probability

中图分类号:

O211.4

程铭,王定成. 考虑一般投资收益和时间相依索赔情形下二维带扰动风险模型的有限时间破产概率渐近估计[J]. 数学物理学报, 2023, 43(5): 1529-1558.

Cheng Ming,Wang Dingcheng. Asymptotic Finite-Time Ruin Probability for a Bidimensional Perturbed Risk Model with General Investment Returns and Time-Dependent Claim Sizes[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1529-1558.

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