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Mathematics > Optimization and Control

arXiv:2404.02871 (math)
[Submitted on 3 Apr 2024 (v1), last revised 20 Nov 2024 (this version, v2)]

Title:Existence and uniqueness results for a mean-field game of optimal investment

Authors:Alessandro Calvia, Salvatore Federico, Giorgio Ferrari, Fausto Gozzi
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Abstract:We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-field equilibrium relies on a priori estimates and the study of nonlinear integral equations, but employs different techniques for the finite and infinite horizon cases. Additionally, we investigate the deterministic counterpart of the mean-field game under study.
Subjects: Optimization and Control (math.OC); Theoretical Economics (econ.TH)
MSC classes: 35Q89, 47H10, 49N10, 49N80, 91A07, 91B38, 91B70
Cite as: arXiv:2404.02871 [math.OC]
  (or arXiv:2404.02871v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2404.02871

Submission history

From: Alessandro Calvia [view email]
[v1] Wed, 3 Apr 2024 17:08:23 UTC (29 KB)
[v2] Wed, 20 Nov 2024 16:05:18 UTC (39 KB)
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