The paper introduces and analyzes N-player and common-noise mean-field games in It\^{o the context of both complete and incomplete financial markets . The players invest in a finite horizon and in a common market by either competitive or homophilous interactions. In both kinds of market environments, the players have  individual risk tolerance coefficients . In the incomplete market setting, these risk tolerances are constants (CARA utilities) , while in the complete market, they are assumed to be wealth-independent random variables depending, among others, on upcoming market information . For all these distinct models , we derive explicit or closed-form solutions for the optimal policies and optimal wealth processes, as well as for the related game values .
In It\^{o N-player and common-noise mean-field games in the context of optimal portfolio choice in a common market . The players invest in a finite horizon and also interact, driven either by competition or homophily. We study an incomplete market model in which the players have constant individual risk tolerance coefficients (CARA utilities) . We also consider the general case of random individual risk tolerances and analyze the related games in a complete market setting. This randomness makes the problem substantially more complex as it leads to (N or a continuum of) auxiliary ''individual'' It\^{o . For all cases , we derive explicit or closed-form solutions for the equilibrium stochastic processes, the optimal state processes, and the values of the games .
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The paper introduces and analyzes
In It\^{o
D
It\^{o
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both complete and incomplete financial markets
optimal portfolio choice in a common market
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in a common market by either competitive or homophilous interactions. In both kinds of market environments,
also interact, driven either by competition or homophily. We study an incomplete market model in which
A
constant
D
. In the incomplete market setting, these risk tolerances are constants
R
, while in the complete market, they are assumed to be wealth-independent random variables depending, among others, on upcoming market information
. We also consider the general case of random individual risk tolerances and analyze the related games in a complete market setting. This randomness makes the problem substantially more complex as it leads to (N or a continuum of) auxiliary ''individual'' It\^{o
R
these distinct models
cases
R
optimal policies and optimal wealth processes, as well as for the related game values
equilibrium stochastic processes, the optimal state processes, and the values of the games