英文标题：
《Worst-Case Expected Shortfall with Univariate and Bivariate Marginals》
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作者：
Anulekha Dhara, Bikramjit Das, and Karthik Natarajan
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最新提交年份：
2017
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英文摘要：
  Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected shortfall when the univariate marginals are known exactly and additional expert information is available in terms of bivariate marginals. Such expert information allows for one to choose from among the many possible parametric families of bivariate copulas. By considering a neighborhood of distance $\\rho$ around the bivariate marginals with the Kullback-Leibler divergence measure, we model the trade-off between conservatism in the worst-case risk measure and confidence in the expert information. Our bound is developed when the only information available on the bivariate marginals forms a tree structure in which case it is efficiently computable using convex optimization. For consistent marginals, as $\\rho$ approaches $\\infty$, the bound reduces to the comonotonic upper bound and as $\\rho$ approaches $0$, the bound reduces to the worst-case bound with bivariates known exactly. We also discuss extensions to inconsistent marginals and instances where the expert information which might be captured using other parameters such as correlations.
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中文摘要：
文献中广泛研究了仅给出随机变量分布有限信息的预期短缺风险的最坏情况界限。在本文中，当单变量边际精确已知，并且可以获得关于双变量边际的额外专家信息时，我们开发了一个关于预期短缺的新的最坏情况界。这样的专家信息允许人们从许多可能的二元copula参数族中进行选择。通过考虑具有Kullback-Leibler散度测度的双变量边缘周围距离$\\ρ$的邻域，我们建立了最坏情况风险测度中的稳健性与专家信息中的置信度之间的权衡模型。我们的界限是在二元边缘上唯一可用的信息形成树结构时发展起来的，在这种情况下，它可以使用凸优化进行有效计算。对于一致的边缘，当$\\rho$接近$\\infty$时，边界降低到共单调上界，当$\\rho$接近$\\0$时，边界降低到最坏情况下的边界，二元变量精确已知。我们还讨论了不一致边缘的扩展，以及可能使用其他参数（如相关性）获取专家信息的实例。
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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：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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