线性宽象限相依^(*)下折现累积理赔尾概率的一致渐近估计  

Uniformly Asymptotic Estimation for the Tail Probability of Discounted Aggregate Claims Under Linearly Wide Quadrant Dependent*Structure

作　　者：钱欢 彭千 QIAN Huan;PENG Qian(School of Mathematical Sciences,Anhui University,Hefei 230601,China;School of Science,Anhui Agricultural University,Hefei 230036,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601 [2]安徽农业大学理学院,安徽合肥230036

出　　处：《安庆师范大学学报（自然科学版）》2021年第4期85-89,共5页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省自然科学基金(1808085MA16)。

摘　　要：在标准的更新风险模型中,理赔额和理赔时间间隔都是独立同分布的随机变量序列,该情形在实际应用中过于理想化。考虑一个非标准的更新风险模型,其中理赔额{X_(i),i≥1}为一列线性宽象限相依^(*)(LWQD^(*))的非负同分布随机变量,其分布属于强次指数族,理赔时间间隔{θ_(i),i≥1}为一列非负独立同分布的随机变量,且与{X_(i),i≥1}相互独立。构造随机变量加权和Kesten型不等式,得到折现累积理赔尾概率的一致渐近估计。In the standard renewal risk model,both claim sizes and claim inter-arrival times are independent and identically distributed random variables,which is too idealized in practice.This paper mainly considers a nonstandard renewal risk model,in which the claim sizes{X_(i),i≥1}are a sequence of nonnegative linearly wide quadrant dependent*(LWQD*)random variables with a common strong subexponential distribution,and their inter-arrival times{θ_(i),i≥1}are a sequence of nonnegative,independent and identically distributed random variables,but independent of{X_(i),i≥1}.By establishing a Kestentype inequality for weighted sums of LWQD*random variables,we obtain the uniformly asymptotic estimation for the tail probability of discounted aggregate claims.

关 键 词：更新风险模型 强次指数分布 Kesten型不等式 一致渐近估计 

分 类 号：O211.4[理学—概率论与数理统计]