Kernel Learning for Mean-Variance Trading Strategies

Abstract: 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.