Cubature on Wiener Space for McKean-Vlasov SDEs with Smooth Scalar Interaction

TL;DR

This paper introduces two novel cubature algorithms on Wiener space for efficiently solving McKean-Vlasov SDEs with smooth scalar interactions, supported by new PDE bounds extending classical results.

Contribution

The paper develops two new cubature algorithms for McKean-Vlasov SDEs and derives sharp gradient bounds for related PDEs, extending classical results.

Findings

Algorithms successfully tested on numerical examples

New PDE bounds of independent interest

Extension of classical Kusuoka-Stroock results

Abstract

We present two cubature on Wiener space algorithms for the numerical solution of McKean-Vlasov SDEs with smooth scalar interaction. The analysis hinges on sharp gradient to time-inhomogeneous parabolic PDEs bounds. These bounds may be of independent interest. They extend the classical results of Kusuoka \& Stroock. Both algorithms are tested through two numerical examples.