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A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation

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  • Zongxia Liang
  • Keyu Zhang

Abstract

This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as benchmarks to evaluate the performance of her decision. We formulate the n-agent game problems and the corresponding mean field game problems under the two utilities. One mean field equilibrium is derived in a closed form in each problem. In each problem with n agents, an approximate Nash equilibrium is then constructed using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained. In addition, we provide some numerical illustrations of our results.

Suggested Citation

  • Zongxia Liang & Keyu Zhang, 2024. "A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation," Papers 2401.15659, arXiv.org.
    • Handle: RePEc:arx:papers:2401.15659
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    References listed on IDEAS

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    7. Guanxing Fu, 2022. "Mean Field Portfolio Games with Consumption," Papers 2206.05425, arXiv.org, revised Dec 2022.
    8. Guanxing Fu, 2023. "Mean field portfolio games with consumption," Mathematics and Financial Economics, Springer, volume 17, number 4, March.
    9. Yushi Hamaguchi, 2019. "Time-inconsistent consumption-investment problems in incomplete markets under general discount functions," Papers 1912.01281, arXiv.org, revised Mar 2021.
    10. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    11. Abel, Andrew B., 1999. "Risk premia and term premia in general equilibrium," Journal of Monetary Economics, Elsevier, vol. 43(1), pages 3-33, February.
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    Cited by:

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