Numerical Methods for the McKean-Vlasov Equation

Abstract

This thesis aims to explore the stochastic differential equation that satisfies the McKean-Vlasov process, in which the coefficients depend on the distribution of the solution itself. Because the McKean-Vlasov equation does not have a closed-form ana- lytical solution, we seek to develop numerical methods that would provide approxima- tions of the McKean-Vlasov process. By looking at autonomous stochastic differen- tial equations with established numerical methods, specifically the Euler-Maruyama method and Milstein's method, we look into developing analogous methods for the McKean-Vlasov process.