Robust Utility Optimization via a GAN Approach

2024-03-22

arXiv.org

AI Summary

This paper addresses model misspecification, transaction costs, and partial observability—key sources of uncertainty in real-world financial markets. Method: We propose a robust utility optimization framework based on Generative Adversarial Networks (GANs), formulating a neural-network-based minimax game between an investor and an adversarial market. Under partial observability—relying solely on historical asset prices—we approximate the worst-case utility maximization. This is the first application of the GAN paradigm to robust portfolio decision-making, accommodating arbitrary continuous utility functions. Contribution/Results: We theoretically establish that path-dependent strategies offer no advantage over Markovian ones. Empirically, our approach matches benchmark optimal policies when known, and significantly outperforms all baselines in the absence of prior optimal solutions. The learned policies exhibit strong generalization and are directly deployable in practice.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Solving robust utility optimization under market uncertainty
• Proposing GAN approach for realistic settings with trading costs
• Comparing performance against optimal and reference strategies

Innovation

• GAN approach for robust utility optimization
• Neural networks model investor and market
• Applicable for continuous utility functions with costs