英文标题：
《A Directional Multivariate Value at Risk》
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作者：
Ra\\\'ul Torres, Rosa E. Lillo and Henry Laniado
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最新提交年份：
2015
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英文摘要：
  In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\\alpha$, the $100\\alpha\\%$ VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is $\\alpha$. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretation as a risk measure. However, its extension to the multivariate framework is not unique because a unique definition of multivariate quantile does not exist. In the current literature, the multivariate quantiles are related to a specific partial order considered in $\\mathbb{R}^{n}$, or to a property of the univariate quantile that is desirable to be extended to $\\mathbb{R}^{n}$. In this work, we introduce a multivariate value at risk as a vector-valued directional risk measure, based on a directional multivariate quantile, which has recently been introduced in the literature. The directional approach allows the manager to consider external information or risk preferences in her/his analysis. We have derived some properties of the risk measure and we have compared the univariate \\textit{VaR} over the marginals with the components of the directional multivariate VaR. We have also analyzed the relationship between some families of copulas, for which it is possible to obtain closed forms of the multivariate VaR that we propose. Finally, comparisons with other alternative multivariate VaR given in the literature, are provided in terms of robustness.
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中文摘要：
在经济学、保险学和金融学中，风险价值（VaR）是一种广泛使用的衡量特定金融资产组合损失风险的指标。对于给定的投资组合、时间范围和概率$\\alpha$，将$100\\alpha\\%$VaR定义为阈值损失值，因此给定时间范围内投资组合的损失超过该值的概率为$\\alpha$。也就是说，它是损失分布的一个分位数，它既具有良好的分析特性，又易于作为风险度量进行解释。然而，它对多元框架的扩展并不是唯一的，因为不存在多元分位数的唯一定义。在目前的文献中，多元分位数与$\\mathbb{R}^{n}$中考虑的特定偏序有关，或者与希望扩展到$\\mathbb{R}^{n}$的单变量分位数的属性有关。在这项工作中，我们引入了一个多元风险值作为向量值方向风险度量，基于一个方向多元分位数，这是最近在文献中引入的。定向方法允许管理者在分析中考虑外部信息或风险偏好。我们导出了风险度量的一些性质，并将边缘上的单变量VaR与定向多元VaR的分量进行了比较。我们还分析了一些连接函数族之间的关系，对于这些连接函数族，我们提出的多元VaR的闭合形式是可能的。最后，在稳健性方面与文献中给出的其他多元VaR进行了比较。
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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：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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