On heavy-tailed risks under Gaussian copula: The effects of marginal transformation

IF 1.4 3区 数学 Q2 STATISTICS & PROBABILITY
Bikramjit Das , Vicky Fasen-Hartmann
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引用次数: 0

Abstract

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a few interesting consequences. First, as the threshold increases, we note that the rate of decay of probabilities of tail sets varies depending on the type of tail sets considered and the Gaussian correlation matrix. Second, we discover that although any multivariate model with a Gaussian copula admits the so-called asymptotic tail independence property, the joint tail behavior under heavier tailed marginal variables is structurally distinct from that under Gaussian marginal variables. The results obtained are illustrated using examples and simulations.

高斯共轭下的重尾风险:边际转换的影响
在本文中,我们计算了边际风险为重尾且依赖结构为高斯共轭的多元尾部风险概率。边际重尾风险采用正则变异建模,这会带来一些有趣的结果。首先,随着阈值的增加,我们注意到尾集概率的衰减率会随着所考虑的尾集类型和高斯相关矩阵的不同而变化。其次,我们发现尽管任何具有高斯共轭的多元模型都具有所谓的渐近尾部独立性,但在重尾边际变量下的联合尾部行为与高斯边际变量下的联合尾部行为在结构上是不同的。我们将通过实例和模拟来说明所获得的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Multivariate Analysis
Journal of Multivariate Analysis 数学-统计学与概率论
CiteScore
2.40
自引率
25.00%
发文量
108
审稿时长
74 days
期刊介绍: Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data. The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of Copula modeling Functional data analysis Graphical modeling High-dimensional data analysis Image analysis Multivariate extreme-value theory Sparse modeling Spatial statistics.
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