# Deep Hedging Under Non-Convexity: Limitations and a Case for AlphaZero

arXiv: https://arxiv.org/abs/2510.01874 · HTML: https://mlsanity.com/paper/2510.01874/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [Monte Carlo Tree Search: A Review of Recent Modifications and Applications](https://mlsanity.com/paper/2103.04931/) (2021)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Deep Hedging of Derivatives Using Reinforcement Learning](https://mlsanity.com/paper/2103.16409/) (2021)
- [Hedging using reinforcement learning: Contextual k-Armed Bandit versus Q-learning](https://mlsanity.com/paper/2007.01623/) (2020)
- [Hedging of Financial Derivative Contracts via Monte Carlo Tree Search](https://mlsanity.com/paper/2102.06274/) (2021)

## Built on by (most cited first, 1 of 1)

- [A Topological Approach to Parameterizing Deep Hedging Networks](https://mlsanity.com/paper/2510.16938/) (2025)

## Abstract (arXiv)

This paper examines replication portfolio construction in incomplete markets - a key problem in financial engineering with applications in pricing, hedging, balance sheet management, and energy storage planning. We model this as a two-player game between an investor and the market, where the investor makes strategic bets on future states while the market reveals outcomes. Inspired by the success of Monte Carlo Tree Search in stochastic games, we introduce an AlphaZero-based system and compare its performance to deep hedging - a widely used industry method based on gradient descent. Through theoretical analysis and experiments, we show that deep hedging struggles in environments where the optimal action-value function is not subject to convexity constraints - such as those involving non-convex transaction costs, capital constraints, or regulatory limitations - converging to local optima. We construct specific market environments to highlight these limitations and demonstrate that AlphaZero consistently finds near-optimal replication strategies. On the theoretical side, we establish a connection between deep hedging and convex optimization, suggesting that its effectiveness is contingent on convexity assumptions. Our experiments further suggest that AlphaZero is more sample-efficient - an important advantage in data-scarce, overfitting-prone derivative markets.