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.

本文提出了一种生成对抗网络方法，用于在普遍和现实环境中近似解决鲁棒效用优化问题，该方法适用于任何连续效用函数，能够在存在交易成本的实际市场环境中使用可观测市场信息进行训练，并表现出与最优参考策略相当的性能，并且对于没有已知最优策略的情况下，该方法优于所有其他参考策略。此外，该文还揭示了在具有交易成本的情况下，学习最优（非）鲁棒投资的生成方法能够生成可以广泛应用于理想化环境的渐近策略的替代选择。