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N-Player and Mean-Field Games in Itˆo-Diffusion Markets with Competitive or Homophilous Interaction

In: Stochastic Analysis, Filtering, and Stochastic Optimization

Author

Listed:
  • Ruimeng Hu

    (University of California, Department of Mathematics and Department of Statistics & Applied Probability)

  • Thaleia Zariphopoulou

    (The University of Texas at Austin, Departments of Mathematics and IROM
    University of Oxford, The Oxford-Man Institute)

Abstract

In Itô-diffusion environments, we introduce and analyze 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” Itô-diffusion markets. 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.

Suggested Citation

  • Ruimeng Hu & Thaleia Zariphopoulou, 2022. "N-Player and Mean-Field Games in Itˆo-Diffusion Markets with Competitive or Homophilous Interaction," Springer Books, in: George Yin & Thaleia Zariphopoulou (ed.), Stochastic Analysis, Filtering, and Stochastic Optimization, pages 209-237, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98519-6_9
    DOI: 10.1007/978-3-030-98519-6_9
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