Mean Field Games with Singular Controls

2016/12/16 by Fu, Guanxing, Horst, Ulrich · 5 citations
#60H30 #91B70 #93E20 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1612.05425

Abstract

This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M₁ topology on the space of càdlàg functions.

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• On Mean-field Singular Stochastic Control Problems
• Entropy Regularization in Mean-Field Games of Optimal Stopping
• Relative compactness of Itô integrals on the M1 Skorokhod space with identification of limits
• Mean Field Game with Reflected Jump Diffusion Dynamics: A Linear Programming Approach
• Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria

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