# Deep Hedging

arXiv: https://arxiv.org/abs/1802.03042 · HTML: https://mlsanity.com/paper/1802.03042/

## Key facts

- Cited by 108 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2018.

## Built on by (most cited first, 30 of 108)

- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Revolutionizing Finance with LLMs: An Overview of Applications and Insights](https://mlsanity.com/paper/2401.11641/) (2024)
- [FinRL: Deep Reinforcement Learning Framework to Automate Trading in Quantitative Finance](https://mlsanity.com/paper/2111.09395/) (2021)
- [PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2308.02585/) (2023)
- [Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality](https://mlsanity.com/paper/2106.08900/) (2021)
- [Policy Optimization for Continuous Reinforcement Learning](https://mlsanity.com/paper/2305.18901/) (2023)
- [Deep Hedging of Derivatives Using Reinforcement Learning](https://mlsanity.com/paper/2103.16409/) (2021)
- [Towards Realistic Market Simulations: a Generative Adversarial Networks Approach](https://mlsanity.com/paper/2110.13287/) (2021)
- [Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes](https://mlsanity.com/paper/2109.03582/) (2021)
- [Time-Correlated Sparsification for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2101.08837/) (2021)
- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Quantum Deep Hedging](https://mlsanity.com/paper/2303.16585/) (2023)
- [Generative modeling for time series via Schr"odinger bridge](https://mlsanity.com/paper/2304.05093/) (2023)
- [Multi-Asset Spot and Option Market Simulation](https://mlsanity.com/paper/2112.06823/) (2021)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [Deep Hedging: Continuous Reinforcement Learning for Hedging of General Portfolios across Multiple Risk Aversions](https://mlsanity.com/paper/2207.07467/) (2022)
- [Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures](https://mlsanity.com/paper/2111.07844/) (2021)
- [Chaotic Hedging with Iterated Integrals and Neural Networks](https://mlsanity.com/paper/2209.10166/) (2022)
- [Deep neural network expressivity for optimal stopping problems](https://mlsanity.com/paper/2210.10443/) (2022)
- [Robust Risk-Aware Option Hedging](https://mlsanity.com/paper/2303.15216/) (2023)
- [Data-Driven Merton's Strategies via Policy Randomization](https://mlsanity.com/paper/2312.11797/) (2023)
- [Robo-Advising: Enhancing Investment with Inverse Optimization and Deep Reinforcement Learning](https://mlsanity.com/paper/2105.09264/) (2021)
- [A Quantum Generative Adversarial Network for distributions](https://mlsanity.com/paper/2110.02742/) (2021)
- [SigFormer: Signature Transformers for Deep Hedging](https://mlsanity.com/paper/2310.13369/) (2023)
- [Hedge Fund Portfolio Construction Using PolyModel Theory and iTransformer](https://mlsanity.com/paper/2408.03320/) (2024)
- [Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programs](https://mlsanity.com/paper/2508.14995/) (2025)
- [A deep learning approach to data-driven model-free pricing and to martingale optimal transport](https://mlsanity.com/paper/2103.11435/) (2021)
- [How Robust are Limit Order Book Representations under Data Perturbation?](https://mlsanity.com/paper/2110.04752/) (2021)
- [Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?](https://mlsanity.com/paper/2204.11231/) (2022)
- [Quant 4.0: Engineering Quantitative Investment with Automated, Explainable and Knowledge-driven Artificial Intelligence](https://mlsanity.com/paper/2301.04020/) (2022)

## Abstract (arXiv)

We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs, market impact, liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We discuss how standard reinforcement learning methods can be applied to non-linear reward structures, i.e. in our case convex risk measures. As a general contribution to the use of deep learning for stochastic processes, we also show that the set of constrained trading strategies used by our algorithm is large enough to ε-approximate any optimal solution. Our algorithm can be implemented efficiently even in high-dimensional situations using modern machine learning tools. Its structure does not depend on specific market dynamics, and generalizes across hedging instruments including the use of liquid derivatives. Its computational performance is largely invariant in the size of the portfolio as it depends mainly on the number of hedging instruments available. We illustrate our approach by showing the effect on hedging under transaction costs in a synthetic market driven by the Heston model, where we outperform the standard "complete market" solution.