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Mean field portfolio games with consumption

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  • Guanxing Fu

    (The Hong Kong Polytechnic University)

Abstract

We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE. Our approach, which is general enough to cover power, exponential and log utilities, relies on martingale optimality principle in Cheridito and Hu (Stochast Dyn 11(02n03):283–299, 2011) and Hu et al. (Ann Appl Probab 15(3):1691–1712, 2005) and dynamic programming principle in Espinosa and Touzi (Math Financ 25(2):221–257, 2015) and Frei and dos Reis (Math Financ Econ 4:161–182, 2011). When the market parameters do not depend on the Brownian paths, we get the unique Nash equilibrium in closed form. As a byproduct, when all market parameters are time-independent, we answer the question proposed in Lacker and Soret (Math Financ Econ 14(2):263–281, 2020): the strong equilibrium obtained in Lacker and Soret (Math Financ Econ 14(2):263–281, 2020) is unique in the essentially bounded space.

Suggested Citation

  • Guanxing Fu, 2023. "Mean field portfolio games with consumption," Mathematics and Financial Economics, Springer, volume 17, number 4, October.
    • Handle: RePEc:spr:mathfi:v:17:y:2023:i:1:d:10.1007_s11579-022-00328-2
    DOI: 10.1007/s11579-022-00328-2
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    References listed on IDEAS

    as
    1. Guanxing Fu & Chao Zhou, 2021. "Mean Field Portfolio Games," Papers 2106.06185, arXiv.org, revised Apr 2022.
    2. Guanxing Fu, 2022. "Mean Field Portfolio Games with Consumption," Papers 2206.05425, arXiv.org, revised Dec 2022.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. 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.
    5. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    6. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utility and market adjustments in relative investment-consumption games of many players," Papers 2012.01235, arXiv.org, revised Mar 2022.
    7. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
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    Cited by:

    1. Dianetti, Jodi & Ferrari, Giorgio & Tzouanas, Ioannis, 2023. "Ergodic Mean-Field Games of Singular Control with Regime-Switching (extended version)," Center for Mathematical Economics Working Papers 681, Center for Mathematical Economics, Bielefeld University.
    2. Dianetti, Jodi, 2023. "Linear-Quadratic-Singular Stochastic Differential Games and Applications," Center for Mathematical Economics Working Papers 678, Center for Mathematical Economics, Bielefeld University.
    3. Zongxia Liang & Jianming Xia & Fengyi Yuan, 2023. "Dynamic portfolio selection for nonlinear law-dependent preferences," Papers 2311.06745, arXiv.org, revised Nov 2023.
    4. Zongxia Liang & Keyu Zhang, 2024. "A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation," Papers 2401.15659, arXiv.org.

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