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$N$-player and Mean-field Games in It\^{o}-diffusion Markets with Competitive or Homophilous Interaction

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  • Ruimeng Hu
  • Thaleia Zariphopoulou

Abstract

In It\^{o}-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'' It\^{o}-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.

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  • Ruimeng Hu & Thaleia Zariphopoulou, 2021. "$N$-player and Mean-field Games in It\^{o}-diffusion Markets with Competitive or Homophilous Interaction," Papers 2106.00581, arXiv.org, revised Jun 2021.
    • Handle: RePEc:arx:papers:2106.00581
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    References listed on IDEAS

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    1. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
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    6. Daniel Lacker & Thaleia Zariphopoulou, 2019. "Mean field and n‐agent games for optimal investment under relative performance criteria," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1003-1038, October.
    7. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.
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    Cited by:

    1. Lijun Bo & Shihua Wang & Xiang Yu, 2021. "Mean Field Game of Optimal Relative Investment with Jump Risk," Papers 2108.00799, arXiv.org, revised Feb 2023.
    2. Ludovic Tangpi & Xuchen Zhou, 2022. "Optimal Investment in a Large Population of Competitive and Heterogeneous Agents," Papers 2202.11314, arXiv.org, revised Feb 2023.
    3. Ming Min & Ruimeng Hu, 2021. "Signatured Deep Fictitious Play for Mean Field Games with Common Noise," Papers 2106.03272, arXiv.org.
    4. Guanxing Fu & Chao Zhou, 2021. "Mean Field Portfolio Games," Papers 2106.06185, arXiv.org, revised Apr 2022.
    5. Lijun Bo & Shihua Wang & Xiang Yu, 2022. "A mean field game approach to equilibrium consumption under external habit formation," Papers 2206.13341, arXiv.org, revised Mar 2024.

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