Kernel Learning for Mean-Variance Trading Strategies

2025-07-14

AI Summary

Classical Markovian mean–variance strategies fail to capture path dependence inherent in asset dynamics and predictive signals. Method: This paper proposes a dynamic, path-dependent trading framework grounded in reproducing kernel Hilbert spaces (RKHS). The policy function is parameterized within an RKHS, enabling flexible incorporation of path features—such as random signatures or neural network embeddings—via custom-designed kernels, while retaining closed-form solutions and avoiding gradient-based optimization. Contribution/Results: Theoretically, the approach unifies kernel learning with pathwise analysis. Empirically, it achieves statistically significant outperformance over classical Markovian benchmarks on both synthetic and real financial market data, demonstrating the modeling efficacy and practical viability of kernel methods in non-Markovian portfolio optimization.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Develop kernel-based dynamic trading strategies under mean-variance optimization
• Compare kernel and signature methods outperforming classical Markovian approaches
• Provide flexible kernel modeling with closed-form solutions avoiding gradient optimization

Innovation

• Kernel-based framework for dynamic trading strategies
• Parameterise strategies in RKHS for flexibility
• Closed-form solutions without gradient optimisation