For the multiplicative background risk model, a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation. In this paper, we investigate the tail asymptotics of the portfolio loss \(\sum _{i=1}^{d}R_iS\), where the stand-alone risk vector \({\mathbf {R}}=(R_1,\ldots ,R_d)\) follows a multivariate regular variation and is independent of the background risk factor S. An explicit asymptotic formula is established for the tail distortion risk measure, and an example is given to illustrate our obtained results.

中文翻译：

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具有多元正则变化的投资组合的尾部扭曲风险度量

对于乘法本底风险模型，使用失真类型风险度量来测量具有多元规则变化的场景概率度量下的投资组合的尾部风险。在本文中，我们研究了投资组合损失\（\ sum _ {i = 1} ^ {d} R_iS \）的尾部渐近性，其中独立风险向量\（{\ mathbf {R}} =（R_1 ，\ ldots，R_D）\）如下多元定期变化，并且独立于背景的危险因素的小号。建立了尾部失真风险度量的显式渐近公式，并给出了一个例子来说明我们获得的结果。