{"ID":2862021,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.00768","arxiv_id":"2510.00768","title":"A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics","abstract":"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.","short_abstract":"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 constrain...","url_abs":"https://arxiv.org/abs/2510.00768","url_pdf":"https://arxiv.org/pdf/2510.00768v1","authors":"[\"Fabio Camilli\",\"Qing Tang\",\"Yong-shen Zhou\"]","published":"2025-10-01T11:00:36Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[\"Large Language Model\",\"Generative Adversarial Network\"]","has_code":false}