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.

翻译：稳健效用优化使投资者能够以结构化方式应对市场不确定性，其目标是最大化最坏情况下的结果。本文提出了一种生成对抗网络（GAN）方法，用于在一般且现实的设定下（近似）求解稳健效用优化问题。具体而言，我们使用神经网络（NN）同时对投资者和市场进行建模，并在极小极大零和博弈框架中对其进行训练。该方法适用于任何连续效用函数，以及仅利用市场可观测信息的包含交易成本的现实市场环境。大规模实证研究表明该方法具有广泛的适用性。当存在最优参考策略时，我们的方法与其性能相当；而在未知最优策略的众多场景中，该方法表现优于所有其他参考策略。此外，从研究中可以得出结论：训练得到的路径依赖策略并不优于马尔可夫策略。最后，我们揭示出：这种用于学习交易成本下最优（非）稳健投资的生成方法，为理想化设定中著名的渐近策略提供了普遍适用的替代方案。