Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance  

作　　者：Yang Yang Shaoying Chen Kam Chuen Yuen 

机构地区：[1]School of Statistics and Data Science,Nanjing Audit University,Nanjing 211815,China [2]Department of Statistics and Actuarial Science,The University of Hong Kong,Hong Kong 999077,China

出　　处：《Science China Mathematics》2024年第1期163-186,共24页中国科学（数学）（英文版）

基　　金：supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China(Grant No.20YJA910006);Natural Science Foundation of Jiangsu Province of China(Grant No.BK20201396);supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX211939);supported by the Research Grants Council of Hong Kong;China(Grant No.HKU17329216)。

摘　　要：This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.

关 键 词：asymptotic joint tail behavior randomly weighted sum heavy-tailed distribution DEPENDENCE insurance risk model 

分 类 号：O213[理学—概率论与数理统计] F840[理学—数学]