Distributional Adversarial Attacks and Training in Deep Hedging

In this paper, we study the robustness of classical deep hedging strategies under distributional shifts by leveraging the concept of adversarial attacks. We first demonstrate that standard deep hedging models are highly vulnerable to small perturbations in the input distribution, resulting in significant performance degradation. Motivated by this, we propose an adversarial training framework tailored to increase the robustness of deep hedging strategies. Our approach extends pointwise adversarial attacks to the distributional setting and introduces a computationally tractable reformulation of the adversarial optimization problem over a Wasserstein ball. This enables the efficient training of hedging strategies that are resilient to distributional perturbations. Through extensive numerical experiments, we show that adversarially trained deep hedging strategies consistently outperform their classical counterparts in terms of out-of-sample performance and resilience to model misspecification. Additional results indicate that the robust strategies maintain reliable performance on real market data and remain effective during periods of market change. Our findings establish a practical and effective framework for robust deep hedging under realistic market uncertainties. 1 Related work. Deep hedging was introduced in [2,28]. Since its introduction, numerous works have studied deep hedging and related machine learning-based hedging methods from different perspectives. Robustness of deep hedging methods has been studied in [10,11,12]. Further directions include tackling complex pricing problems [29,30,31], targeting improved efficiency [32,33] or general initial portfolios [34], alternative reinforcement learning frameworks [35,36,37,38], empirical approaches [39,40], or implementations on quantum hardware [41]. We refer to the surveys [42,43] for a comprehensive overview.

Parallel to this, distributionally robust optimization (DRO) has emerged as a framework for decisionmaking under model uncertainty, with Wasserstein-based methods offering both theoretical guarantees and computational tractability [13,17,18]. In machine learning, adversarial training provides another robustness perspective, where worst-case perturbations improve generalization [19,20,21,22]. Recent works extend pointwise adversarial attacks to the distributional setting [23,24,25,26,27], thereby connecting adversarial training methods with DRO formulations.