This was part of Applications to Financial Engineering

## Mean field game of mutual holding

Nizar Touzi, Ecole Polytechnique
Monday, December 6, 2021

Abstract: We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding $N-$agent model. The induced mean field dynamics appear naturally in a form which is not covered by standard McKean-Vlasov stochastic differential equations. We study the corresponding mean field game of mutual holding in the absence of common noise. Our main result provides existence of an explicit equilibrium of this mean field game, defined by a bang-bang control consisting in holding