A mean-field model of optimal investment
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2024
- DOI:
- 10.48550/arXiv.2404.02871
- arXiv:
- arXiv:2404.02871
- Bibcode:
- 2024arXiv240402871C
- Keywords:
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- Mathematics - Optimization and Control;
- Economics - Theoretical Economics;
- 35Q89;
- 47H10;
- 49N10;
- 49N80;
- 91A07;
- 91B38;
- 91B70