# Computation of optimal transport and related hedging problems via penalization and neural networks

arXiv: https://arxiv.org/abs/1802.08539 · HTML: https://mlsanity.com/paper/1802.08539/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2018.

## Built on by (most cited first, 7 of 7)

- [A deep learning approach to data-driven model-free pricing and to martingale optimal transport](https://mlsanity.com/paper/2103.11435/) (2021)
- [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)
- [Fitted value iteration methods for bicausal optimal transport](https://mlsanity.com/paper/2306.12658/) (2023)
- [Application of Self-Supervised Learning to MICA Model for Reconstructing Imperfect 3D Facial Structures](https://mlsanity.com/paper/2304.04060/) (2023)
- [Neural networks can detect model-free static arbitrage strategies](https://mlsanity.com/paper/2306.16422/) (2023)
- [Improved model-free bounds for multi-asset options using option-implied information and deep learning](https://mlsanity.com/paper/2404.02343/) (2024)

## Abstract (arXiv)

This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, martingale optimal transport, portfolio optimization under uncertainty and generative adversarial networks that showcase the generality and effectiveness of the approach.