具有复合相依的离散时间风险模型的尾部渐近及数值模拟  

Tail Asymptotic of Discrete-Time Risk Model with Compound Dependence and Numerical Simulation

作　　者：井浩杰 彭江艳[1] 蒋智权 JING Haojie;PENG Jiangyan;JIANG Zhiquan(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》2021年第6期569-584,共16页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:71871046);四川省科技计划项目(批准号:2021YFQ0007);国家自然科学基金项目(批准号:72033002)的资助.

摘　　要：本文研究具有复合相依的离散时间风险模型.保险公司进行风险和无风险投资导致了任意相依的随机折现因子.索赔额服从单边线性过程,其中噪声项遵循成对渐近独立,噪声项和随机折现因子相互独立.假设噪声项不必同分布并且是非负的随机变量,其分布分别为F_(1),F_(2),……,F_(n).当平均分布n^(-1)∑_(i=1)^nF_(i)是重尾时,本文得到离散时间风险模型的有限时间破产概率的渐近估计.最后通过蒙特卡洛模拟验证了本文的结果.This paper considers a discrete-time risk model with compound dependence.The risk-free and risky investments of an insurer lead to arbitrarily dependent stochastic discount factors.The claim-sizes are assumed to follow a one-sided linear process with pairwise asymptotically independent innovations.The innovations and the stochastic discount factors are mutually independent.We assume that innovations are not necessarily identically distributed nonnegative random variables with distributionsF_(1),F_(2),……,F_(n)..When the average distribution n^(-1)∑_(i=1)^nF_(i) is heavy-tailed,we establish some asymptotic estimates for the finite-time ruin probabilities of this discrete time risk model.We demonstrate our obtained results through a crude Monte Carlo simulation.

关 键 词：单边线性过程 成对渐近独立 重尾 数值模拟 

分 类 号：O211.4[理学—概率论与数理统计]