Economically responsible mitigation of multivariate extreme risks-such as extreme rainfall over large areas, large simultaneous variations in many stock prices, or widespread breakdowns in transportation systems-requires assessing the resilience of the systems under plausible stress scenarios. This paper uses Extreme Value Theory (EVT) to develop a new approach to simulating such multivariate extreme events. Specifically, we assume that after transformation to a standard scale the distribution of the random phenomenon of interest is multivariate regular varying and use this to provide a sampling procedure for extremes on the original scale. Our procedure combines a Wasserstein-Aitchison Generative Adversarial Network (WA-GAN) to simulate the tail dependence structure on the standard scale with joint modeling of the univariate marginal tails on the original scale. The WA-GAN procedure relies on the angular measure-encoding the distribution on the unit simplex of the angles of extreme observations-after transformation to Aitchison coordinates, which allows the Wasserstein-GAN algorithm to be run in a linear space. Our method is applied both to simulated data under various tail dependence scenarios and to a financial data set from the Kenneth French Data Library. The proposed algorithm demonstrates strong performance compared to existing alternatives in the literature, both in capturing tail dependence structures and in generating accurate new extreme observations.

翻译：对多元极端风险（例如大范围极端降雨、多只股票价格同时大幅波动或交通系统大规模瘫痪）进行经济合理的缓解，需要评估系统在合理压力情景下的韧性。本文利用极值理论（EVT）提出了一种模拟此类多元极端事件的新方法。具体而言，我们假设在变换至标准尺度后，所关注随机现象的分布具有多元正则变化性，并利用此性质提供原始尺度上极值的抽样程序。我们的方法结合了Wasserstein-Aitchison生成对抗网络（WA-GAN）来模拟标准尺度上的尾部相依结构，并对原始尺度上的单变量边缘尾部进行联合建模。WA-GAN方法依赖于角测度（编码极端观测值角度在单位单纯形上的分布）经变换至Aitchison坐标后，使得Wasserstein-GAN算法能在线性空间中运行。我们将该方法应用于多种尾部相依情景下的模拟数据以及来自Kenneth French数据图书馆的金融数据集。与文献中现有方法相比，所提算法在捕捉尾部相依结构和生成准确的新极端观测值方面均表现出优越性能。