ExceedGAN: simulation above extreme thresholds using Generative Adversarial Networks

This paper devises a novel neural-inspired approach for simulating multivariate extremes. Specifically, we propose a GAN-based generative model for sampling multivariate data exceeding large thresholds, giving rise to what we refer to as the ExceedGAN algorithm. Our approach is based on approximating marginal log-quantile functions using feedforward neural networks with eLU activation functions specifically introduced for bias correction. An error bound is provided on the margins, assuming a th order condition from extreme value theory. The numerical experiments illustrate that ExceedGAN outperforms competitors, both on synthetic and real-world data sets.