Simulation of multivariate extremes: A Wasserstein–Aitchison GAN approach

Stéphane Lhaut, Holger Rootzén and Johan Segers
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Stéphane Lhaut: Université catholique de Louvain, LIDAM/ISBA, Belgium
Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2026007, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: 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.

Keywords: Aitchison coordinates; Angular measure; Extreme value theory; Generative adversarial networks; Generative AI for extremes; Multivariate analysis; Wasserstein distance (search for similar items in EconPapers)
Date: 2026-02-06
Note: In: Extremes, 2026
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2026007

DOI: 10.1007/s10687-026-00530-1

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