Paper: arXiv 2609.34474

Authors: Jean-Loup Dupret, Donatien Hainaut, Edouard Motte

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical framework for deep kernel hedging, including a generalized representer theorem and convergence guarantees. It balances this theoretical depth with empirical evaluation on both synthetic and real data, demonstrating robust performance. The novelty lies in combining deep learning flexibility with kernel method inductive bias for hedging, particularly in low-data regimes.

Research Flowchart

  flowchart TD
    A[Research Goal: Deep Kernel Hedging] --> B{Key Methodology: Combine Deep Learning & Kernel Methods};
    B --> C{Inputs: Market Data, Path-Dependent Info (Signatures)};
    C --> D[Computational Process: Minimized Regularized Empirical Risk];
    D --> E{Optimization: Finite-Dimensional Problem (Representer Theorem)};
    E --> F[Scalability: Random Fourier Features Approximation];
    F --> G{Outcomes: Competitive & Robust Hedging Performance};
    G --> H[Benefits: Expressive Neural Reps + Kernel Inductive Bias];