Deep Asymptotic Expansion: Application to Financial Mathematics

Abstract

The paper proposes a new computational scheme for diffusion semigroups based on an asymptotic expansion with weak approximation and deep learning algorithm to solve high-dimensional Kolmogorov partial differential equations (PDEs). In particular, we give a spatial approximation for the solution of $d -$dimensional PDEs on a range $[a,b]^{d}$ without suffering from the curse of dimensionality.