# Kernel Learning for Mean-Variance Trading Strategies

arXiv: https://arxiv.org/abs/2507.10701 · HTML: https://mlsanity.com/paper/2507.10701/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [The Signature Kernel is the solution of a Goursat PDE](https://mlsanity.com/paper/2006.14794/) (2020)
- [Fast Sketching of Polynomial Kernels of Polynomial Degree](https://mlsanity.com/paper/2108.09420/) (2021)
- [Neural signature kernels as infinite-width-depth-limits of controlled ResNets](https://mlsanity.com/paper/2303.17671/) (2023)
- [Signature Methods in Stochastic Portfolio Theory](https://mlsanity.com/paper/2310.02322/) (2023)
- [Accumulation of Sub-Sampling Matrices with Applications to Statistical Computation](https://mlsanity.com/paper/2103.04031/) (2021)
- [Rough kernel hedging](https://mlsanity.com/paper/2501.09683/) (2025)
- [Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals](https://mlsanity.com/paper/2308.15135/) (2023)
- [Randomized Signature Methods in Optimal Portfolio Selection](https://mlsanity.com/paper/2312.16448/) (2023)
- [Signature Maximum Mean Discrepancy Two-Sample Statistical Tests](https://mlsanity.com/paper/2506.01718/) (2025)
- [A User's Guide to textttKSig: GPU-Accelerated Computation of the Signature Kernel](https://mlsanity.com/paper/2501.07145/) (2025)
- [Markowitz portfolio selection for multivariate affine and quadratic Volterra models](https://mlsanity.com/paper/2006.13539/) (2020)

## Built on by (most cited first, 1 of 1)

- [Deep kernel hedging](https://mlsanity.com/paper/2609.34474/) (2026)

## Abstract (arXiv)

In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we parameterise trading strategies as functions in a reproducing kernel Hilbert space (RKHS), enabling a flexible and non-Markovian approach to optimal portfolio problems. We compare this with the signature-based framework of (Futter, Horvath, Wiese, 2023) and demonstrate that both significantly outperform classical Markovian methods when the asset dynamics or predictive signals exhibit temporal dependencies for both synthetic and market-data examples. Using kernels in this context provides significant modelling flexibility, as the choice of feature embedding can range from randomised signatures to the final layers of neural network architectures. Crucially, our framework retains closed-form solutions and provides an alternative to gradient-based optimisation.