Mean field and n-player games in Ito-diffusion markets under forward performance criteria

Abstract

We study n-player games of portfolio choice in general common Ito-diffusion markets under relative performance criteria and time monotone forward utilities. We, also, consider their continuum limit which gives rise to a forward mean field game with unbounded controls in both the drift and volatility terms. Furthermore, we allow for general (time monotone) preferences, thus departing from the homothetic case, the only case so far analyzed. We produce explicit solutions for the optimal policies, the optimal wealth processes and the game values, and also provide representative examples for both the finite and the mean field game.

Keywords

Mean field game / n-player game / Ito-diffusion / Forward performance criteria

Acknowledgements

This work was presented at seminars and workshops at Columbia, Oxford University, University of Michigan, Ann Arbor, the 9th International Colloquium on BSDE and Mean Field systems, Annecy and at the Institute for Mathematical Innovation and Statistics (IMSI), University of Chicago. The author would like to thank the participants for fruitful comments and suggestions. She would also like to thank IMSI for its hospitality during the Spring 2022 and Spring 2023 long programs, during which most of this work was completed.

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