Kernel Learning for Mean-Variance Trading Strategies

Paper: arXiv 2507.10701

Authors: Owen Futter, Nicola Muca Cirone, Blanka Horvath

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.

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 6.0/10 (capped from 8.0: transaction costs not modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematics including reproducing kernel Hilbert spaces, kernel trick, and path-dependent PDEs for optimization, while also demonstrating robust empirical validation with synthetic data and market data backtests that explicitly compare against baseline methods.

Research Flowchart

  flowchart TD
  A["Research Goal: Develop a kernel-based framework for dynamic,<br>path-dependent trading strategies under mean-variance optimisation"] --> B{"Methodology"};
  B --> C["Parameterise strategies as functions in<br>Reproducing Kernel Hilbert Space RKHS"];
  C --> D["Compare with Signature-based<br>framework of Futter et al."];
  D --> E["Computational Process:<br>Derive closed-form solutions vs gradient-based methods"];
  
  subgraph Data/Inputs
      F["Synthetic Asset Dynamics<br>Market Data with Temporal Dependencies"]
  end
  
  E <--> F;
  F --> G["Key Findings/Outcomes"];
  
  G --> H["RKHS & Signatures significantly<br>outperform classical Markovian methods"];
  G --> I["Kernels provide modelling flexibility<br>via feature embeddings e.g., randomised signatures, NN layers"];
  G --> J["Framework retains closed-form solutions<br>alternative to gradient-based optimisation"];

Cited References (370)

1. A Closed-Form Execution Strategy to Target Volume Weighted Average Price (2016) — link
2. A comprehensive review of deterministic models and applications for mean-variance portfolio optimization (2019) — link
3. A Course on Rough Paths With an introduction to regularity structures (2020)
4. A data-driven neural network approach to dynamic factor investing with transaction costs (2021) — link
5. A five-factor asset pricing model (2015) — link
6. A Generalized Representer Theorem (2001) — link
7. A Global-in-Time Neural Network Approach to Dynamic Portfolio Optimization (2024) — link
8. A Kernel for Time Series Based on Global Alignments. (2007) — link

21 of 370 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.