A mean-field model for optimal investment.

In this talk, I will introduce a class of continuous-time mean-field games that aim to describe games of optimal investment. I will consider the case where the representative firm can increase its capital stock via costly investments and aims at optimizing its discounted operating profit, which depends on the distribution of the capital stocks of all firms. I will discuss this family of models both in a finite and in an infinite time horizon setting and I will also present some applications (e.g., vintage capital models) where an infinite dimensional formulation is required. I will analyze a specific linear-quadratic one-dimensional case, where it is possible to prove the existence of an equilibrium. This is joint work in progress with Giorgio Ferrari (Universität Bielefeld), Salvatore Federico (Università di Genova), and Fausto Gozzi (LUISS University).