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

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外文摘要：This paper studies the joint tail behavior of two randomly weighted sums ∑mi=1ΘiXi and ∑nj=1 θjYj for some m,n ∈ N∪ {∞},in which the primary random variables {Xi;i ∈ N} and {Yi;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 {Xi;i ∈ N},{Yi;i ∈ N} and{Θi,θi;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.

外文关键词：

asymptotic joint tail behaviorrandomly weighted sumheavy-tailed distributiondependenceinsurance risk model

作者：

Yang Yang、Shaoying Chen、Kam Chuen Yuen

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作者单位：

School of Statistics and Data Science,Nanjing Audit University,Nanjing 211815,China

Department of Statistics and Actuarial Science,The University of Hong Kong,Hong Kong 999077,China

基金：

Humanities and Social Sciences Foundation of the Ministry of Education of ChinaNatural Science Foundation of Jiangsu Province of ChinaPostgraduate Research and Practice Innovation Program of Jiangsu Province of ChinaResearch Grants Council of Hong Kong,China

项目编号：

20YJA910006BK20201396KYCX21-1939HKU17329216

出版年：

2024

DOI：

10.1007/s11425-022-2030-5

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

CSTPCD

影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(1)

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