Rough kernel hedging

Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging problems. We make minimal assumptions about market dynamics by modelling them as general geometric rough paths, yielding a fully model-free approach. Furthermore, through a representer theorem, we provide theoretical guarantees on the existence and uniqueness of a global minimum for the resulting optimization problem and derive an analytic solution under highly general loss functions. Similar to the popular deep hedging approach, but in a more rigorous fashion, our method can also incorporate additional features via the underlying operator-valued kernel, such as trading signals, news analytics, and past hedging decisions, closely aligning with true machine-learning practice.