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In this talk, I present results on stationary mean-field games with singular controls for a Markov-modulated Ito-diffusion, in which the representative player interacts with a long-time conditional weighted average of the population through a discounted performance criterion. This class of games finds natural applications in the context of irreversible production expansion in dynamic oligopolies, where the dynamics of the production capacity depends on the economy's business cycles modeled through a continuous-time Markov chain. We prove existence and uniqueness of the mean-field stationary equilibrium and characterize it through a system of nonlinear equations. Along the way, explicit results for the joint stationary distribution of the controlled production capacity and the Markov chain at equilibrium are also derived. A detailed numerical analysis allows to understand the dependency of the mean-field equilibrium with respect to the model's parameters. This is based on a joint ongoing work with René Aid and Matteo Basei.

Biography: Giorgio Ferrari is professor for Mathematical Finance at the Center for Mathematical Economics (IMW) at Bielefeld University since 2017. He obtained his Ph.D. in Mathematics for Economic-Financial Applications at the University of Rome "La Sapienza" in 2012. He then moved to IMW where he was first post-doctoral researcher (2012-2016), and then Junior-Professor (2016-2017). His research interests lie in the field of stochastic control theory, stochastic games, and their applications to Economics and Finance. Particular attention is devoted to dynamic stochastic optimization problems and games involving singular controls and stopping rules, and to the analysis of the corresponding free-boundary problems.