具有相依风险的有限时间破产概率的渐近估计和CMC模拟  

Asymptotic Estimates of Finite-Time Ruin Probabilities with Dependent Risks and CMC Simulations

作　　者：白明艳 彭江艳[1] 井浩杰 BAI Mingyan;PENG Jiangyan;JING Haojie(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu,611731,China)

机构地区：[1]电子科技大学数学科学学院,成都611731

出　　处：《应用概率统计》2020年第6期569-585,共17页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.71871046,71501025);the Applied Basic Project of Sichuan Province(Grant No.2016JY0257)。

摘　　要：我们考虑了一个具有相依结构的离散时间风险模型,其中索赔额{Xm}n≥1遵循一个具有独立同分布(i.i.d.)噪声项{εn}n≥1的单边线性过程,且噪声项和金融风险形成了一系列独立同分布的副本,这些副本是来自于具有相依结构的一个随机对(ε,Y).当乘积εY具有重尾分布时,我们建立了这种离散时间风险模型中破产概率的一些渐近估计.最后,我们使用原始的蒙特卡罗(CMC)模拟来验证我们的结果.We consider a discrete-time risk model with dependence structures,where the claimsizes {Xn}n≥1 follow a one-sided linear process with independent and identically distributed(i.i.d.)innovations {εn}n≥1,and the innovations and financial risks form a sequence of independent and identically distributed copies of a random pair(ε,Y) with dependent components.When the productεY has a heavy-tailed distribution,we establish some asymptotic estimates of the ruin probabilities in this discrete-time risk model.Finally,we use a Crude Monte Carlo(CMC) simulation to verify our results.

关 键 词：渐近估计 单边线性过程 相依风险 乘积 重尾分布 

分 类 号：O211.4[理学—概率论与数理统计]