  Robust utility optimization enables an investor to deal with market
uncertainty in a structured way, with the goal of maximizing the worst-case
outcome. In this work, we propose a generative adversarial network (GAN)
approach to (approximately) solve robust utility optimization problems in
general and realistic settings. In particular, we model both the investor and
the market by neural networks (NN) and train them in a mini-max zero-sum game.
This approach is applicable for any continuous utility function and in
realistic market settings with trading costs, where only observable information
of the market can be used. A large empirical study shows the versatile
usability of our method. Whenever an optimal reference strategy is available,
our method performs on par with it and in the (many) settings without known
optimal strategy, our method outperforms all other reference strategies.
Moreover, we can conclude from our study that the trained path-dependent
strategies do not outperform Markovian ones. Lastly, we uncover that our
generative approach for learning optimal, (non-) robust investments under
trading costs generates universally applicable alternatives to well known
asymptotic strategies of idealized settings.
