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

Washington State University, Pullman WA

Investigators

Abstract

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.