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3 avril 2024
- 2404.02871
Mots-clés
Mathematics - Optimization and Control Economics - Theoretical Economics 35Q89, 47H10, 49N10, 49N80, 91A07, 91B38, 91B70Sujets proches
Balancing (Physics) Balance (Physics) BalanceCiter ce document
Alessandro Calvia et al., « A mean-field model of optimal investment », arXiv - économie
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Résumé
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.