Mean Field Game of Mutual Holding with Common Noise*

We consider the mean field game of cross--holding introduced in Djete and Touzi [3] in the context where the equity value dynamics are affected by a common noise. In contrast with [3], the problem exhibits the standard paradigm of mean--variance trade off. Our crucial observation is to search for equilibrium solutions of our mean field game among those models which satisfy an appropriate notion of no--arbitrage. Under this condition, it follows that the representative agent optimization step is reduced to a standard portfolio optimization problem with random endowment.