相依结构下重尾随机变量和条件分布尾渐近性态

Tail asymptotic behavior of conditional distribution for sums of heavy-tailed random variables under dependence structure

给定n个非负基本随机变量,其分布属于一致变化重尾分布族,以及另外n个非负任意相依的加权随机变量,但是与基本随机变量相互独立,在一类相依结构下,本文得到了基本随机变量和与加权随机变量和条件分布尾若干渐近公式,并给出了它们在风险度量中的一个应用,推广了相关文献的结论。

Give n nonnegative primary random variables with distributions from consistently-varying heavy - tailed class, and another n nonnegative weighted random variables with no dependence assumption among them, but independent of primary random variables. Under a class of dependence structure, some tail asymptotic formulas for conditional distribution of sums of primary random variables and weighted random variables are investigated in this paper, then as an application, the results are used to risk measure. The obtained results extend the corresponding ones in literature.