AMC-SS: Asymptotic Analysis of Extreme Risks with High-Dimensional Tail Dependence Modeling

这笔赠款为高维分布的极端相关性分析提供了资金，这些相关性结构由Vine Copula描述，这些相关性结构是由二元分布的基本构件构建的。多变量极值之间的极值相关性可以用多元极值理论的谱或强度度量来刻画。边际单变量极值所具有的参数特征在多变量极值的相依结构中消失了，因此丰富的相依性质在很大程度上仍未被探索，特别是对于由Vine Copulas建模的大型随机系统。本研究着眼于尾部相关性方法与多变量规则变异之间的相互作用，通过根据潜在的图结构探索尾部相关性的递归方案，发展了高维图形模型的极值理论。该图的极值理论被用来定量地分析大型随机系统中尾部相关性的出现和蔓延，并对高维多变量极值的尾部相关性引发的极端系统风险进行易于处理的渐近估计。在数据网络、金融风险管理和全球气候变化等不同领域观察到了异常相关性。全球金融危机和气候变化最能说明尾部依赖带来的极端风险及其具有传染性的不利影响。这个项目的目标是对这些对复杂社会的安全、安保和可持续性至关重要的紧迫问题进行基础研究。该项目的成功完成将导致对极端风险进行高效和准确的估计，并将增强了解、检测和缓解极端风险的研究能力，这将促进有效的灾难风险管理，造福社会。

This grant provides funding for the extremal dependence analysis of high-dimensional distributions with dependence structures described by vine copulas that are built from basic building blocks of bivariate distributions. The extremal dependence among multivariate extremes can be characterized in terms of the spectral or intensity measure using Multivariate Extreme Value Theory. The parametric feature, enjoyed by marginal univariate extreme values, vanishes in the dependence structure of multivariate extremes, and thus rich dependence properties remain largely unexplored, especially for large stochastic systems modeled by vine copulas. Focusing on the interplay between the tail dependence method and multivariate regular variation, the investigator in this research develops an extremal value theory for high-dimensional graphical models, such as vine copulas, by exploring recursive schemes for tail dependence according to underlying graph structures. This graphical extreme value theory is then used to quantitatively analyze tail dependence emergence and contagion in large stochastic systems, and to develop tractable asymptotic estimates for extremal system risks fueled by tail dependence of high-dimensional multivariate extremes.Extremal dependence has been observed in diverse fields, such as data networks, financial risk management, and global climate change, to name just a few. Extreme risk fueled by tail dependence and its contagious adverse effects have been best illustrated from the global financial crisis and climate change. This project targets a fundamental research for these pressing issues that are important to safety, security and sustainability of complex societies. Successful completion of the project will lead to efficient and accurate estimations for extreme risks and will enhance research capabilities to understand, detect, and mitigate extreme risks, which will facilitate effective catastrophe risk management that benefits society.