A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics
We study continuous-time heterogeneous agent models cast as Mean Field Games, in the Aiyagari-Bewley-Huggett framework. The model couples a Hamilton-Jacobi-Bellman equation for individual optimization with a Fokker-Planck-Kolmogorov equation for the wealth distribution. We establish a comparison principle for constrained viscosity solutions of the HJB equation and propose a semi-Lagrangian (SL) scheme for its numerical solution, proving convergence via the Barles-Souganidis method. A policy iteration algorithm handles state constraints, and a dual SL scheme is used for the FPK equation. Numerical methods are presented in a fully discrete, implementable form.
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