A deep learning-based high-order operator splitting method for high-dimensional nonlinear parabolic PDEs via Malliavin calculus: application to CVA computation

Abstract

The paper introduces a deep learning-based high-order operator splitting method for nonlinear parabolic partial differential equations (PDEs) by using a Malliavin calculus approach. Through the method, a solution of a nonlinear PDE is accurately approximated even when the dimension of the PDE is high. As an application, the method is applied to the CVA computation in high-dimensional finance models. Numerical experiments performed on GPUs show the efficiency of the proposed method.