# Robust pricing and hedging of options on multiple assets and its numerics

arXiv: https://arxiv.org/abs/1909.03870 · HTML: https://mlsanity.com/paper/1909.03870/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2019.

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

- [Chaotic Hedging with Iterated Integrals and Neural Networks](https://mlsanity.com/paper/2209.10166/) (2022)
- [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)
- [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)

We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two numerical methods to solve such problems: using discretisation and linear programming applied to the primal side and using penalisation and deep neural networks optimisation applied to the dual side. We prove convergence for our methods and compare their numerical performance. We show how adding further information about call option prices at additional maturities can be incorporated and narrows down the no-arbitrage pricing bounds. Finally, we obtain structural results for the case of the payoff given by a weighted sum of covariances between the assets.