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.

参考文献 17

1	Fotios L . Precise large deviations for strong subexponential distributions and applications on a multi risk model. Commun Stat-Theor M, 2018, 48 (20): 5175- 5190
2	Ng K W , Tang Q , Yan J , Yang H . Precise large deviations for sums of random variables with consistently varying tails. J Appl Probab, 2004, 165 (1): 93- 107
3	Tang Q , Su C , Jiang T , Zhang J . Large deviations for heavy-tailed random sums in compound renewal model. Statist Probab Lett, 2001, 52 (1): 91- 100 doi: 10.1016/S0167-7152(00)00231-5
4	Shen X , Tian H . Precise large deviations for sums of two-dimensional random vectors with dependent components of heavy tails. Commun Stat Theor M, 2016, 45 (21): 6357- 6368 doi: 10.1080/03610926.2013.839794
5	Wang S , Wang W . Precise large deviations for sums of random variables with consistent variation in dependent multi-risk models. Commun Stat Theor M, 2013, 42 (24): 4444- 4459 doi: 10.1080/03610926.2011.648792
6	肖鸿民, 王占魁. 基于客户来到的二维风险模型的精细大偏差. 数学物理学报, 2020, 40A (4): 1108- 1120 doi: 10.3969/j.issn.1003-3998.2020.04.025
	Xiao H M , Wang Z K . The precise large deviations of a bidimensional risk model based on customer arrival. Acta Math Sci, 2020, 40A (4): 1108- 1120 doi: 10.3969/j.issn.1003-3998.2020.04.025
7	Asimit A V , Badescu A L . Extremes on the discounted aggregate claims in a time dependent risk model. Scand Actuar J, 2010, 2010 (2): 93- 104 doi: 10.1080/03461230802700897
8	Chen Y , Yuen K C . Precise large deviations of aggregate claims in a size-dependent renewal risk model. Insurance Math Econom, 2012, 51 (2): 457- 461 doi: 10.1016/j.insmatheco.2012.06.010
9	Bi X , Zhang S . Precise large deviations of aggregate claims in a risk model with regression-type size-dependence. Statist Probab Lett, 2013, 83 (10): 2248- 2255 doi: 10.1016/j.spl.2013.06.009
10	Li R , Bi X , Zhang S . Large deviations for sums of claims in a general renewal risk model with the regression dependent structure. Statist Probab Lett, 2020, 165, 108857 doi: 10.1016/j.spl.2020.108857
11	Embrechts P, Klüppelberg C, Mikosch T. Modelling Extremal Events for Insurance and Finance. New York: Springer, 1997
12	Tang Q , Tsitsiashvili G . Precise estimates for the ruin probability in finite horizon in a discretetime model with heavy-tailed insurance and financial risks. Stochastic Process Appl, 2003, 108 (2): 299- 325 doi: 10.1016/j.spa.2003.07.001
13	Bingham N H , Goldie C M , Teugels J L . Regular Variation. Cambridge: Cambridge University Press, 1987
14	Roger B N. An Introduction to Copulas. New York: Springer, 2006
15	Wang K , Wang Y , Gao Q . Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate. Methodol Comput Appl Probab, 2013, 15 (1): 109- 124 doi: 10.1007/s11009-011-9226-y
16	Korchevsky V M , Petrov V V . On the strong law of large numbers for sequences of dependent random variables. Vestnik St Petersburg Univ Math, 2010, 43 (3): 143- 147 doi: 10.3103/S1063454110030040
17	Shen X , Fu K , Zhong X . Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model. Appl Math J Chinese Univ, 2018, 33 (4): 491- 502 doi: 10.1007/s11766-018-3579-8

[1]	肖鸿民,王占魁. 基于客户来到的二维风险模型的精细大偏差[J]. 数学物理学报, 2020, 40(4): 1108-1120.
[2]	韦晓; 于金酉; 胡亦钧. 变保费率扰动风险模型的有限时间破产概率和大偏差[J]. 数学物理学报, 2007, 27(4): 616-623.