Mean Field Portfolio Games with Consumption
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We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between the Nash equilibrium of the game and the solution to some FBSDE, which is proved to be equivalent to some BSDE. Our approach, which is general enough to cover power, exponential and log utilities, relies on martingale optimality principle in [3,9] and dynamic programming principle in [6,7]. When the market parameters do not depend on the Brownian paths, we get the unique Nash equilibrium in closed form. As a byproduct, when all market parameters are time-independent, we answer the question proposed in : the strong equilibrium obtained in  is unique in the essentially bounded space.
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