用核方法构建能捕捉时间依赖的动态投资组合，效果优于传统模型。
Kernel Learning for Mean-Variance Trading Strategies
- 将交易策略建模为核希尔伯特空间函数，实现非马尔可夫动态优化。
- 在合成与真实市场数据上均显著优于经典马尔可夫方法。
- 支持闭式解，适合需快速计算的量化交易场景。
本文提出一种基于核函数的框架，用于在均值-方差优化准则下构建动态、路径依赖的投资策略。基于（Muca Cirone and Salvi, 2025）的理论，我们将交易策略参数化为再生核希尔伯特空间（RKHS）中的函数，从而实现灵活且非马尔可夫的最优投资组合求解。与（Futter, Horvath, Wiese, 2023）的签名框架对比，两者在资产动态或预测信号存在时间依赖性的合成及真实市场数据中均显著超越经典马尔可夫方法。该框架通过选择不同特征嵌入（如随机签名或神经网络末层）实现强大建模灵活性，同时保持闭式解，提供无需梯度优化的替代方案。
原文摘要 · Abstract (English)
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.
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