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摘要翻译：
在本文中，我们引入了经典的单变量风险值(VaR)在多变量环境中的两个可供选择的扩展。提出的两个多元VaR是向量值测度，与基础风险投资组合的维度相同。下正交VaR由多元分布函数的水平集构造，而上正交VaR由多元生存函数的水平集构造。已经导出了几个属性。特别地，我们证明了这些风险测度都满足正齐性和平移不变性。给出了单变量风险测度与多元VaR分量的比较。我们还分析了边际分布的变化、依赖结构的变化和风险水平的变化对这些度量的影响。在阿基米德Copulas类中给出了插图。
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英文标题：
《On Multivariate Extensions of Value-at-Risk》
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作者：
Areski Cousin (SAF), Elena Di Bernadino (SAF)
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最新提交年份：
2013
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas the upper-orthant VaR is constructed from level sets of multivariate survival functions. Several properties have been derived. In particular, we show that these risk measures both satisfy the positive homogeneity and the translation invariance property. Comparison between univariate risk measures and components of multivariate VaR are provided. We also analyze how these measures are impacted by a change in marginal distributions, by a change in dependence structure and by a change in risk level. Illustrations are given in the class of Archimedean copulas.
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PDF链接：
https://arxiv.org/pdf/1111.1349
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