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We study the optimal portfolio selection problem under relative performancecriteria in the market model with random coefficients from the perspective ofmany players game theory. We consider five random coefficients which consist ofthree market parameters which are used in the risky asset price modeling andtwo preference parameters which are related to risk attitude and impact ofrelative performance. We focus on two cases; either all agents have ConstantAbsolute Risk Aversion (CARA) risk preferences or all agents have ConstantRelative Risk Aversion (CRRA) risk preferences for their investmentoptimization problem. For each case, we show that the forward Nash equilibriumand the mean field equilibrium exist for the n-agent game and the correspondingmean field stochastic optimal control problem, respectively. To extend then-agent game to the continuum of players game, we introduce a measure dependentforward relative performance process and apply an optimization over controlleddynamics of McKean-Vlasov type. We conclude that our optimal portfolio formulasextend the corresponding results of the market model with constantcoefficients.

Optimal portfolio selection of many players under relative performance criteria in the market model with random coefficients