  The estimation of loss distributions for dynamic portfolios requires the
simulation of scenarios representing realistic joint dynamics of their
components, with particular importance devoted to the simulation of tail risk
scenarios. We propose a novel data-driven approach that utilizes Generative
Adversarial Network (GAN) architecture and exploits the joint elicitability
property of Value-at-Risk (VaR) and Expected Shortfall (ES). Our proposed
approach is capable of learning to simulate price scenarios that preserve tail
risk features for benchmark trading strategies, including consistent statistics
such as VaR and ES.
  We prove a universal approximation theorem for our generator for a broad
class of risk measures. In addition, we show that the training of the GAN may
be formulated as a max-min game, leading to a more effective approach for
training. Our numerical experiments show that, in contrast to other data-driven
scenario generators, our proposed scenario simulation method correctly captures
tail risk for both static and dynamic portfolios.
