Current browse context:
math.NA
Change to browse by:
References & Citations
Mathematics > Numerical Analysis
Title: A path-dependent PDE solver based on signature kernels
(Submitted on 18 Mar 2024)
Abstract: We develop a provably convergent kernel-based solver for path-dependent PDEs (PPDEs). Our numerical scheme leverages signature kernels, a recently introduced class of kernels on path-space. Specifically, we solve an optimal recovery problem by approximating the solution of a PPDE with an element of minimal norm in the signature reproducing kernel Hilbert space (RKHS) constrained to satisfy the PPDE at a finite collection of collocation paths. In the linear case, we show that the optimisation has a unique closed-form solution expressed in terms of signature kernel evaluations at the collocation paths. We prove consistency of the proposed scheme, guaranteeing convergence to the PPDE solution as the number of collocation points increases. Finally, several numerical examples are presented, in particular in the context of option pricing under rough volatility. Our numerical scheme constitutes a valid alternative to the ubiquitous Monte Carlo methods.
Submission history
From: Alexandre Pannier [view email][v1] Mon, 18 Mar 2024 12:47:19 GMT (2519kb,D)
Link back to: arXiv, form interface, contact.