Mean Field Utility Maximization Game with Partial Information
We study a mean field utility maximization game, where each player manages a stock whose return process depends on a hidden factor, which cannot be observed by the manager. The manager needs to infer the return process and rewrite the dynamics of the stock price based on the information available to her. Moreover, each manager is concerned not only with her own terminal wealth but also with the relative performance of her competitiors. We use the probabilistic approach to consider exponential and power utilities. Due to the mean field interaction and the nature of the game, the FBSDE systems characterizing the equilibria of our problem become coupled mean-field FBSDEs with possibly quadratic growth. We establish the well-posedness result of the mean-field FBSDEs in some suitable BMO space; firstly we work on a short time interval and secondly the local solution is extended to an arbitrary interval by considering the corresponding variational FBSDEs.