# Rough kernel hedging

arXiv: https://arxiv.org/abs/2501.09683 · HTML: https://mlsanity.com/paper/2501.09683/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2025.

## Built on by (most cited first, 9 of 9)

- [Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models](https://mlsanity.com/paper/2505.17761/) (2025)
- [Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programs](https://mlsanity.com/paper/2508.14995/) (2025)
- [ParallelFlow: Parallelizing Linear Transformers via Flow Discretization](https://mlsanity.com/paper/2504.00492/) (2025)
- [Kernel Learning for Mean-Variance Trading Strategies](https://mlsanity.com/paper/2507.10701/) (2025)
- [Novelty detection on path space](https://mlsanity.com/paper/2512.03243/) (2025)
- [Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs](https://mlsanity.com/paper/2605.30213/) (2026)
- [Advances in Neural Controlled Differential Equations](https://mlsanity.com/paper/2607.05280/) (2026)
- [Tradable Ito Signatures: A Model-Free, Interpretable Framework for Dynamic Hedging](https://mlsanity.com/paper/2608.18120/) (2026)
- [Deep kernel hedging](https://mlsanity.com/paper/2609.34474/) (2026)

## Abstract (arXiv)

Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging problems. We make minimal assumptions about market dynamics by modelling them as general geometric rough paths, yielding a fully model-free approach. Furthermore, through a representer theorem, we provide theoretical guarantees on the existence and uniqueness of a global minimum for the resulting optimization problem and derive an analytic solution under highly general loss functions. Similar to the popular deep hedging approach, but in a more rigorous fashion, our method can also incorporate additional features via the underlying operator-valued kernel, such as trading signals, news analytics, and past hedging decisions, closely aligning with true machine-learning practice.