Robust Utility Optimization via a GAN Approach

ArXiv ID: 2403.15243 “View on arXiv”

Authors: Unknown

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.

Keywords: utility optimization, generative adversarial networks, robust optimization, portfolio management, trading costs

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts such as stochastic calculus, minimax optimization, and deep learning theory, representing high math complexity. It includes a large empirical study with comparative metrics against reference strategies, demonstrating substantial implementation and data-driven validation.

  flowchart TD
    A["Research Goal: Robust Utility Optimization via GAN Approach"] --> B["Methodology: GAN with Investor & Market NNs"]
    B --> C["Input: Realistic Market Data with Trading Costs"]
    C --> D["Process: Mini-Max Zero-Sum Game Training"]
    D --> E{"Outcomes"}
    E --> F["Performs on par with optimal strategies where available"]
    E --> G["Outperforms other strategies in unknown settings"]
    E --> H["Markovian strategies suffice over path-dependent ones"]
    E --> I["Generates universal alternatives to idealized asymptotic strategies"]