关键词: 多元极值, 参数模型, 极值统计学, 极值理论, 尾部相依性

Abstract: Due to the frequent co-occurrences of extremes, research on multivariate extremes has become the theoretical frontier and focus in extreme value statistics. This paper systematically surveys the recent developments on parametric modeling for multivariate extremes, including the classical multivariate extreme value theory, Ledford-Tawn-Ramos’ approach and Heffernan and Tawn’s conditional approach, and etc., and extensively analyzes the pros and cons of these models and possible issues of theoretical improvement. Besides, we also investigate their current applications in finance, and suggest that the potential areas of future applications might be in financial contagion, portfolios and systemic risk management, and etc.

Key words: Multivariate, extremes, Parametric, model, Extreme, value, statistics, Extreme, value, theory, Tail, dependence