# Deep kernel hedging

arXiv: https://arxiv.org/abs/2609.34474 · HTML: https://mlsanity.com/paper/2609.34474/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 57 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees](https://mlsanity.com/paper/1804.09893/) (2018)
- [Approximation Bounds for Random Neural Networks and Reservoir Systems](https://mlsanity.com/paper/2002.05933/) (2020)
- [Learning to Learn Kernels with Variational Random Features](https://mlsanity.com/paper/2006.06707/) (2020)
- [Parsimonious Online Learning with Kernels via Sparse Projections in Function Space](https://mlsanity.com/paper/1612.04111/) (2016)
- [Rough kernel hedging](https://mlsanity.com/paper/2501.09683/) (2025)
- [Deep Kernel Learning via Random Fourier Features](https://mlsanity.com/paper/1910.02660/) (2019)
- [How to tune the RBF SVM hyperparameters?: An empirical evaluation of 18 search algorithms](https://mlsanity.com/paper/2008.11655/) (2020)
- [End-to-end Kernel Learning via Generative Random Fourier Features](https://mlsanity.com/paper/2009.04614/) (2020)
- [Hedging with memory: shallow and deep learning with signatures](https://mlsanity.com/paper/2508.02759/) (2025)
- [Signature approach for pricing and hedging path-dependent options with frictions](https://mlsanity.com/paper/2511.23295/) (2025)
- [KrigHedge: Gaussian Process Surrogates for Delta Hedging](https://mlsanity.com/paper/2010.08407/) (2020)
- [Kernel Learning for Mean-Variance Trading Strategies](https://mlsanity.com/paper/2507.10701/) (2025)

## Abstract (arXiv)

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.