发表机构
University of Amsterdam; ETH Zurich; Université Catholique de Louvain（阿姆斯特丹大学; 苏黎世联邦理工学院; 鲁汶大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出深度核套期保值框架，结合深度学习灵活性与核方法归纳偏置，通过神经网络参数化核并采用随机傅里叶近似降低计算成本，在低数据场景下实现稳健的套期保值性能。
AI 中文摘要
我们引入了一个深度核套期保值框架，该框架将深度学习的灵活性与核方法的结构性归纳偏置相结合。套期保值泛函被限制在一个再生核希尔伯特空间中，其核通过输入特征的神经网络嵌入进行参数化。该框架在凸损失函数下最小化正则化经验风险，并可通过截断的时间增强签名特征来适应路径依赖信息。我们推导了联合套期保值问题的广义表示定理，将经验优化简化为有限维问题。为进一步降低与大核矩阵相关的计算成本，我们开发了一种可扩展的随机傅里叶特征近似方法，并建立了收敛保证。随机傅里叶参数仅采样一次，并在整个训练过程中保持不变，而深度核则通过学到的神经表示适应市场数据。我们在合成数据和真实数据上评估了所提出的深度核方法的性能，并将其与标准核方法和经典深度套期保值架构进行了比较。数值结果表明，该方法在低数据场景下尤其具有竞争性和稳健的套期保值性能，这凸显了将表达性神经表示与核方法的归纳偏置相结合的优势。
英文摘要
We introduce a deep kernel hedging framework that combines the flexibility of deep learning with the structural inductive bias of kernel methods. The hedging functional is restricted to a reproducing kernel Hilbert space whose kernel is parameterized through a neural network embedding of the input features. The framework minimizes a regularized empirical risk under convex loss functions and can accommodate path-dependent information through truncated time-augmented signature features. We derive a generalized representer theorem for the joint hedging problem, reducing the empirical optimization to a finite-dimensional problem. To further reduce the computational cost associated with large kernel matrices, we develop a scalable random Fourier feature approximation and establish convergence guarantees. The random Fourier parameters are sampled once and remain fixed throughout training, while the deep kernel adapts to market data through the learned neural representation. We evaluate the performance of the proposed deep kernel approach on both synthetic and real data and compare it with standard kernel methods and classical deep hedging architectures. Numerical results indicate competitive and robust hedging performance, particularly in low-data regimes, which highlights the benefits of combining expressive neural representations with the inductive bias of kernel methods.
