# Distributional Adversarial Attacks and Training in Deep Hedging

arXiv: https://arxiv.org/abs/2508.14757 · HTML: https://mlsanity.com/paper/2508.14757/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 23 of 23)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Neural networks for option pricing and hedging: a literature review](https://mlsanity.com/paper/1911.05620/) (2019)
- [Deep Hedging of Derivatives Using Reinforcement Learning](https://mlsanity.com/paper/2103.16409/) (2021)
- [Quantum Deep Hedging](https://mlsanity.com/paper/2303.16585/) (2023)
- [Wasserstein distributional robustness of neural networks](https://mlsanity.com/paper/2306.09844/) (2023)
- [Option Hedging with Risk Averse Reinforcement Learning](https://mlsanity.com/paper/2010.12245/) (2020)
- [Sensitivity analysis of Wasserstein distributionally robust optimization problems](https://mlsanity.com/paper/2006.12022/) (2020)
- [Robust Risk-Aware Option Hedging](https://mlsanity.com/paper/2303.15216/) (2023)
- [Robust Generalization despite Distribution Shift via Minimum Discriminating Information](https://mlsanity.com/paper/2106.04443/) (2021)
- [Fast Deep Hedging with Second-Order Optimization](https://mlsanity.com/paper/2410.22568/) (2024)
- [Hedging with Linear Regressions and Neural Networks](https://mlsanity.com/paper/2004.08891/) (2020)
- [Enhancing Adversarial Robustness via Uncertainty-Aware Distributional Adversarial Training](https://mlsanity.com/paper/2411.02871/) (2024)
- [Wasserstein distributional adversarial training for deep neural networks](https://mlsanity.com/paper/2502.09352/) (2025)

## Built on by (most cited first, 2 of 2)

- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Robust Control under Stationary Ambiguity](https://mlsanity.com/paper/2608.04832/) (2026)

## Abstract (arXiv)

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.