标题： 核学习用于均值-方差交易策略 显示英文标题

标题： Kernel Learning for Mean-Variance Trading Strategies

摘要： 在本文中，我们开发了一个基于核的框架，在均值-方差优化准则下构建动态、路径依赖的交易策略。 基于(Muca Cirone和Salvi, 2025)的理论结果，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，从而实现一种灵活且非马尔可夫的方法来解决最优投资组合问题。 我们将其与(Futter, Horvath, Wiese, 2023)的基于符号的框架进行比较，并证明当资产动态或预测信号表现出时间依赖性时，无论是合成数据还是市场数据示例，两者都显著优于经典马尔可夫方法。 在此背景下使用核函数提供了显著的建模灵活性，因为特征嵌入的选择可以从随机符号到神经网络架构的最后几层。 至关重要的是，我们的框架保留了显式解，并提供了梯度优化的替代方案。 显示英文摘要

摘要： 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.