Mean field game of mutual holding with common noise

We consider the Mean Field Game of Mutual Holding introduced in the paper of Djete & Touzi (2020), within a framework where equity value dynamics are affected by common noise. The problem formulation uncovers a No-Arbitrage (NA) condition that is necessary for the existence of equilibria and streamlines their investigation. The presentation is structured into two parts:

The first part is dedicated to the one-period model. We explicitly characterize the NA condition and the mean field equilibria related to a mean-variance criterion.

In the second part, we extend the study to a continuous-time setting. Here, we use a weak notion of the NA condition, under which the representative agent's optimization step is reduced to a standard portfolio optimization problem with random endowment.

This is a joint work with Mao Fabrice Djete and Nizar Touzi.