Abstract In this paper we consider the sum S n ξ ≔ ξ 1 + … + ξ n of (possibly dependent and nonidentically distributed) real-valued random variables ξ 1 , … , ξ n with dominatedly varying distributions. Assuming that the ξ k ’s follow the dependence structure, similar to the asymptotic independence, we obtain the asymptotic lower and upper bounds for the tail moment E ( ( S n ξ ) m 1 { S n ξ > x } ) , where m is a nonnegative integer, improving the bounds of Leipus et al. (2019). We also consider the case of nonnegative random variables. Using the obtained results, we get the asymptotic estimations for the Haezendonck-Goovaerts risk measure in two examples of sums with regularly varying and dominatedly varying (but not regularly varying) increments.

中文翻译：

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具有重尾增量的和的高阶矩尾及其在 Haezendonck-Goovaerts 风险测度中的应用

摘要 在本文中，我们考虑了分布占主导地位的实值随机变量 ξ 1 , ... , ξ n 的和 S n ξ ≔ ξ 1 + … + ξ n （可能是相关的和非相同分布的）实值随机变量 ξ 1 , … , ξ n 。假设 ξ k 遵循依赖结构，类似于渐近独立性，我们得到尾矩 E ( ( S n ξ ) m 1 { S n ξ > x } ) 的渐近上下界，其中 m是一个非负整数，改进了 Leipus 等人的界限。(2019)。我们还考虑了非负随机变量的情况。使用获得的结果，我们在两个示例中获得了 Haezendonck-Goovaerts 风险度量的渐近估计，这些示例具有规律变化和主要变化（但不规律变化）的增量。