Partial differential equation models in macroeconomics
The purpose of this article is to get mathematicians interested in studying a number of partial
differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come …
differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come …
Mean field games and applications: Numerical aspects
The theory of mean field games aims at studying deterministic or stochastic differential
games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field …
games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field …
Income and wealth distribution in macroeconomics: A continuous-time approach
Abstract We recast the Aiyagari–Bewley–Huggett model of income and wealth distribution in
continuous time. This workhorse model—as well as heterogeneous agent models more …
continuous time. This workhorse model—as well as heterogeneous agent models more …
A machine learning framework for solving high-dimensional mean field game and mean field control problems
Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent
models for the efficient analysis of massive populations of interacting agents. Their areas of …
models for the efficient analysis of massive populations of interacting agents. Their areas of …
Numerical methods for mean field games and mean field type control
M Lauriere - Mean field games, 2021 - books.google.com
Mean Field Games (MFG) have been introduced to tackle games with a large number of
competing players. Considering the limit when the number of players is infinite, Nash …
competing players. Considering the limit when the number of players is infinite, Nash …
[图书][B] Regularity theory for mean-field game systems
This book brings together several recent developments on the regularity theory for mean-
field game systems. We detail several classes of methods and present a concise overview of …
field game systems. We detail several classes of methods and present a concise overview of …
Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Optimal control of diffusion processes is intimately connected to the problem of solving
certain Hamilton–Jacobi–Bellman equations. Building on recent machine learning inspired …
certain Hamilton–Jacobi–Bellman equations. Building on recent machine learning inspired …
Mean field games models—a brief survey
The mean-field framework was developed to study systems with an infinite number of
rational agents in competition, which arise naturally in many applications. The systematic …
rational agents in competition, which arise naturally in many applications. The systematic …
An introduction to mean field game theory
These notes are an introduction to Mean Field Game (MFG) theory, which models differential
games involving infinitely many interacting players. We focus here on the Partial Differential …
games involving infinitely many interacting players. We focus here on the Partial Differential …
Computational methods for first-order nonlocal mean field games with applications
We introduce a novel framework to model and solve first-order mean field game systems
with nonlocal interactions, extending the results in [L. Nurbekyan and J. Saúde, Port. Math …
with nonlocal interactions, extending the results in [L. Nurbekyan and J. Saúde, Port. Math …