# A deep learning approach to data-driven model-free pricing and to martingale optimal transport

arXiv: https://arxiv.org/abs/2103.11435 · HTML: https://mlsanity.com/paper/2103.11435/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 64 references that are in the map.
- First posted on arXiv 21 Mar 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-dual Algorithm](https://mlsanity.com/paper/1904.04546/) (2019)
- [Computation of optimal transport and related hedging problems via penalization and neural networks](https://mlsanity.com/paper/1802.08539/) (2018)
- [Computational Methods for Martingale Optimal Transport problems](https://mlsanity.com/paper/1710.07911/) (2017)
- [Robust risk aggregation with neural networks](https://mlsanity.com/paper/1811.00304/) (2018)
- [Low-Rank plus Sparse Decomposition of Covariance Matrices using Neural Network Parametrization](https://mlsanity.com/paper/1908.00461/) (2019)
- [Robust pricing and hedging of options on multiple assets and its numerics](https://mlsanity.com/paper/1909.03870/) (2019)
- [Model-free bounds for multi-asset options using option-implied information and their exact computation](https://mlsanity.com/paper/2006.14288/) (2020)
- [Arbitrage and duality in nondominated discrete-time models](https://mlsanity.com/paper/1305.6008/) (2013)
- [Martingale transport with homogeneous stock movements](https://mlsanity.com/paper/1908.10242/) (2019)
- [On the stability of the martingale optimal transport problem: A set-valued map approach](https://mlsanity.com/paper/2102.02718/) (2021)

## Built on by (most cited first, 6 of 6)

- [Chaotic Hedging with Iterated Integrals and Neural Networks](https://mlsanity.com/paper/2209.10166/) (2022)
- [Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradient](https://mlsanity.com/paper/2210.13193/) (2022)
- [Detecting data-driven robust statistical arbitrage strategies with deep neural networks](https://mlsanity.com/paper/2203.03179/) (2022)
- [Machine learning for option pricing: an empirical investigation of network architectures](https://mlsanity.com/paper/2307.07657/) (2023)
- [Neural networks can detect model-free static arbitrage strategies](https://mlsanity.com/paper/2306.16422/) (2023)
- [Hedging and Pricing Structured Products Featuring Multiple Underlying Assets](https://mlsanity.com/paper/2411.01121/) (2024)

## Abstract (arXiv)

We introduce a novel and highly tractable supervised learning approach based on neural networks that can be applied for the computation of model-free price bounds of, potentially high-dimensional, financial derivatives and for the determination of optimal hedging strategies attaining these bounds. In particular, our methodology allows to train a single neural network offline and then to use it online for the fast determination of model-free price bounds of a whole class of financial derivatives with current market data. We show the applicability of this approach and highlight its accuracy in several examples involving real market data. Further, we show how a neural network can be trained to solve martingale optimal transport problems involving fixed marginal distributions instead of financial market data.