Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model  

作　　者：SHEN Xin-mei FU Ke-ang ZHONG Xue-ting 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology [2]School of Statistics and Mathematics, Zhejiang Gongshang University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2018年第4期491-502,共12页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(Nos.11571058&11301481);Humanities and Social Science Foundation of the Ministry of Education of China(No.17YJC910007);Zhejiang Provincial Natural Science Foundation of China(No.LY17A010004);Fundamental Research Funds for the Central Universities(No.DUT17LK31)

摘　　要：Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.Consider a multidimensional renewal risk model, in which the claim sizes {X_k, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.

关 键 词：Precise large deviation SIZE-DEPENDENT Consistent variation Multidimensional risk model Renewal counting process 

分 类 号：O1[理学—数学]