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Mean Field Equilibrium Asset Pricing Model with Habit Formation

Author

Listed:
  • Masaaki Fujii

    (Faculty of Economics, The University of Tokyo)

  • Masashi Sekine

    (Graduate School of Economics, The University of Tokyo)

Abstract

This paper presents an asset pricing model in an incomplete market involving a large number of heterogeneous agents, based on the mean field game theory. The primary objective of this study is to derive the equilibrium risk premium process endogenously by considering the optimal consumption-investment problem and the market clearing condition. In the model, we incorporate habit formation in consumption preferences, which has been widely used to explain various phenomena in financial economics. In order to characterize the market-clearing equilibrium, we derive a quadratic-growth mean field backward stochastic differential equation (BSDE) and study its well-posedness and asymptotic behavior in the large population limit. Additionally, we introduce an exponential quadratic Gaussian reformulation of the asset pricing model, in which the solution is obtained in a semi-analytic form.

Suggested Citation

  • Masaaki Fujii & Masashi Sekine, 2024. "Mean Field Equilibrium Asset Pricing Model with Habit Formation," CIRJE F-Series CIRJE-F-1229, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2024cf1229
    as

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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2024/2024cf1229.pdf
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    References listed on IDEAS

    as
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    3. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field Equilibrium Price Formation with Exponential Utility," CIRJE F-Series CIRJE-F-1210, CIRJE, Faculty of Economics, University of Tokyo.
    4. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    5. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," CARF F-Series CARF-F-559, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Masaaki Fujii & Akihiko Takahashi, 2014. "Making mean-variance hedging implementable in a partially observable market," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1709-1724, October.
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    13. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," Papers 2304.07108, arXiv.org, revised Oct 2023.
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