A mean-field model of optimal investment - Alessandro Calvia; Salvatore Federico; Giorgio Ferrari; Fausto Gozzi (Bielefeld University, Center for Mathematical Economics (IMW), 2024)
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.
urn:nbn:de:0070-pub-29883840
Keywords: C02; C61; C62; C72; D25; D41; 330; mean-field games; mean-field equilibrium; forward-backward ODEs; optimal investment; price formation