# Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning

arXiv: https://arxiv.org/abs/2302.09176 · HTML: https://mlsanity.com/paper/2302.09176/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 17 Feb 2023.

## Builds on (most cited first, 3 of 3)

- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Universal Approximation Theorems for Differentiable Geometric Deep Learning](https://mlsanity.com/paper/2101.05390/) (2021)
- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)

## Abstract (arXiv)

We consider the problem of simultaneously approximating the conditional distribution of market prices and their log returns with a single machine learning model. We show that an instance of the GDN model of Kratsios and Papon (2022) solves this problem without having prior assumptions on the market's "clipped" log returns, other than that they follow a generalized Ornstein-Uhlenbeck process with a priori unknown dynamics. We provide universal approximation guarantees for these conditional distributions and contingent claims with a Lipschitz payoff function.