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

这项拨款为高维分布的极端依赖分析提供资金，这些高维分布的依赖结构由vine copula描述，该copula是由二元分布的基本构建块构建的。多元极值之间的极值依赖性可以用多元极值理论的光谱或强度度量来表征。边际单变量极值所具有的参数特征在多变量极值的依赖结构中消失，因此丰富的依赖性质在很大程度上仍未被探索，特别是对于由vine copula建模的大型随机系统。本研究着眼于尾依赖方法与多变量正则变化之间的相互作用，通过探索基于底层图结构的尾依赖递归格式，发展了高维图模型（如藤轴）的极值理论。然后将该图形极值理论用于定量分析大型随机系统中的尾部依赖性出现和传染，并对由高维多元极值尾部依赖性引发的极端系统风险进行可处理的渐近估计。在数据网络、金融风险管理和全球气候变化等多个领域都观察到极端依赖。全球金融危机和气候变化最能说明由尾部依赖引发的极端风险及其传染性负面影响。本项目针对这些对复杂社会的安全、保障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有助于对极端风险进行有效和准确的估计，并将增强研究能力，以了解、检测和减轻极端风险，从而促进有效的巨灾风险管理，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.