A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911187754549248 |
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| author | Camilli, Fabio Tang, Qing Zhou, Yong-shen |
| author_facet | Camilli, Fabio Tang, Qing Zhou, Yong-shen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics Camilli, Fabio Tang, Qing Zhou, Yong-shen Optimization and Control Numerical Analysis 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. |
| title | A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2510.00768 |