双相依结构下离散时间风险模型的破产概率渐近估计及数值模拟  

Asymptotic Estimates for Ruin Probabilities of a Discrete-time Risk Model Under Double Dependence Structures and Numerical Simulations

作　　者：井浩杰 彭江艳[1] 蒋智权 鲍倩 JING Haojie;PENG Jiangyan;JIANG Zhiquan;BAO Qian(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu,Sichuan,611731,P.R.China)

机构地区：[1]电子科技大学数学科学学院,成都四川611731

出　　处：《数学进展》2021年第2期290-302,共13页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.71871046,71501025)。

摘　　要：本文研究了具有双相依结构及重尾索赔噪声项的离散时间风险模型的有限时间破产概率.在该模型中,索赔额服从具有独立同分布噪声项的单边线性过程;保险公司的风险投资和无风险投资导致的随机折现因子与单边线性过程的噪声项相依.保险公司单期保费收入是恒定的常数,当单边线性过程的噪声项服从重尾分布时,本文得到离散时间风险模型有限时间破产概率的渐近估计.最后利用蒙特卡罗模拟方法验证所得结果.The finite-time ruin probability of a discrete-time risk model with double dependence structures and heavy-tailed cl aim-innovations is investigated in this paper.The claim sizes follow a one-sided linear process with independent and identically distributed innovations,The risk-free and risky investments of an insurer lead to stochastic discount factors,which are dependent of the claim-innovations.The premium rate is a constant.When the innovations have a heavy-tailed distribution,we establish an asymptotic estimate for the finite-time ruin probability of a discrete-time risk model.Finally,we use a Monte Carlo(MC)simulation to verify our results.

关 键 词：双相依结构 单边线性过程 离散时间风险模型 重尾噪声项 

分 类 号：O211.4[理学—概率论与数理统计]