Kernel Learning for Dynamic Mean-Variance Trading Strategies

Summary

The article presents a kernel-based method for constructing dynamic trading strategies under a mean-variance objective. It represents strategies as functions in a reproducing kernel Hilbert space, allowing decisions to depend on the history of market signals rather than only the current state. This offers a flexible approach to portfolio problems when asset dynamics or predictive signals have temporal dependence.

The framework is compared with a signature-based method and classical Markovian approaches. In synthetic and market-data examples, both non-Markovian approaches are reported to perform significantly better when temporal dependencies are present. Kernel feature choices can include randomized signatures or neural-network layers, while the method retains closed-form solutions instead of relying on gradient-based optimization. The excerpt does not specify datasets, metrics, or the size and robustness of the reported gains.

Key ideas

• The method parameterizes trading policies as functions in a reproducing kernel Hilbert space.
• History-dependent strategies can address temporal dependencies that Markovian methods may miss.
• The article compares kernel learning with signature-based strategies and classical Markovian approaches.
• It reports better performance in synthetic and market-data examples when temporal dependence is present.
• The framework offers closed-form solutions and flexible feature embeddings.

Tags

# Kernel Learning for Mean-Variance Trading Strategies


# Kernel Learning for Mean-Variance Trading Strategies









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.