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

被引:0
|
作者
Yang Yang
Shaoying Chen
Kam Chuen Yuen
机构
[1] Nanjing Audit University,School of Statistics and Data Science
[2] The University of Hong Kong,Department of Statistics and Actuarial Science
来源
Science China Mathematics | 2024年 / 67卷
关键词
asymptotic joint tail behavior; randomly weighted sum; heavy-tailed distribution; dependence; insurance risk model; 62P05; 62E20; 91B05;
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中图分类号
学科分类号
摘要
This paper studies the joint tail behavior of two randomly weighted sums ∑i=1m ΘiXi and ∑j=1nθjYj 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.
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页码:163 / 186
页数:23
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