二维回归相依风险模型的精细大偏差

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 934-942.

二维回归相依风险模型的精细大偏差

陈振龙¹(),刘扬¹(),傅可昂^1,^2,*()

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

收稿日期:2021-03-23 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 傅可昂 E-mail:zlchen@zjgsu.edu.cn;sukey07828@163.com;fukeang@hotmail.com
作者简介:陈振龙, E-mail: zlchen@zjgsu.edu.cn|刘扬, E-mail: sukey07828@163.com
基金资助:
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）

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

Zhenlong Chen¹(),Yang Liu¹(),Ke-ang Fu^1,^2,*()

¹ School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
² Department of Statistics, Zhejiang University City College, Hangzhou 310015

Received:2021-03-23 Online:2022-06-26 Published:2022-05-09
Contact: Ke-ang Fu E-mail:zlchen@zjgsu.edu.cn;sukey07828@163.com;fukeang@hotmail.com
Supported by:
the NSFC(11971432);the NSSFC(20BTJ050);the NSF of Zhejiang Province(LY21G010003);the Zhejiang Province Focuses on the Construction of Advantageous and Characteristic Disciplines in Universities(Statistics of Zhejiang Industrial and Commercial University)

摘要/Abstract

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$ \{\vec{X}_k=(X_{1k}, X_{2k})^T, $ $k\ge 1\}$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.

关键词: 二维风险模型, 一致变化尾, 精细大偏差, 回归相依

Abstract:

In this paper, we consider a non-standard bidimensional risk model, in which the claim sizes $ \{\vec{X}_k=(X_{1k}, X_{2k})^T, $ $k\ge 1\}$ 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.

Key words: Bidimensional risk model, Consistently varying tail, Precise large deviations, Regression dependence

中图分类号:

O211.4

陈振龙,刘扬,傅可昂. 二维回归相依风险模型的精细大偏差[J]. 数学物理学报, 2022, 42(3): 934-942.

Zhenlong Chen,Yang Liu,Ke-ang Fu. Precise Large Deviations for a Bidimensional Risk Model with the Regression Dependent Structure[J]. Acta mathematica scientia,Series A, 2022, 42(3): 934-942.

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