二维回归相依风险模型的精细大偏差  

Precise Large Deviations for a Bidimensional Risk Model with the Regression Dependent Structure

作　　者：陈振龙[1] 刘扬 傅可昂[1,2] Chen Zhenlong;Liu Yang;Fu Ke-ang(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018;Department of Statistics,Zhejiang University City College,Hangzhou 310015)

机构地区：[1]浙江工商大学统计与数学学院,杭州310018 [2]浙大城市学院计算机与计算科学学院,杭州310015

出　　处：《数学物理学报（A辑）》2022年第3期934-942,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971432);国家社会科学基金(20BTJ050);浙江省自然科学基金(LY21G010003);浙江省重点建设高校优势特色学科(浙江工商大学统计学)~。

摘　　要：该文讨论了一类非标准二维风险模型,其中索赔额向量{X^(→)_(k)=(X1k,X2k)^(T),k≥1}是独立同分布的非负随机向量序列,向量内部两分量之间相依,且向量与索赔发生时间间隔之间还存在回归相依关系.在索赔额向量边际分布具有一致变化尾的条件下,得到该二维回归相依风险模型损失和的精细大偏差.In this paper,we consider a non-standard bidimensional risk model,in which the claim sizes{X^(→)_(k)=(X1k,X2k)^(T),k≥1}form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other,and there exists a regression dependent structure between these vectors and the inter-arrival times.By assuming that the univariate marginal distributions of claim vectors have consistently varying tails,we obtain the precise large deviation formulas for the bidimensional risk model with the regression dependent structure.

关 键 词：二维风险模型 一致变化尾 精细大偏差 回归相依 

分 类 号：O211.4[理学—概率论与数理统计]