Forward utilities and Mean-field games under relative performance concerns
We introduce the concept of mean field games for agents using Forward utilities of CARA type to study a family of portfolio management problems under relative performance concerns. Under asset specialization of the fund managers, we solve the forward-utility finite player game and the forward-utility mean-field game. We study best response and equilibrium strategies in the single common stock asset and the asset specialization with common noise. As an application, we draw on the core features of the forward utility paradigm and discuss a problem of time-consistent mean-field dynamic model selection in sequential time-horizons.
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