Robust Utility Optimization via a GAN Approach
This work addresses robust investment optimization for financial practitioners by providing a versatile, data-driven approach in realistic market conditions, though it is incremental as it adapts existing GAN frameworks to this domain.
The authors tackled robust utility optimization under market uncertainty by proposing a GAN-based method that models investor and market strategies with neural networks in a mini-max game, applicable to continuous utility functions and realistic settings with trading costs. Empirical results show the method performs on par with optimal reference strategies when available and outperforms others in settings without known optima, while also revealing that path-dependent strategies do not outperform Markovian ones.
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.