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Mean field equilibrium asset pricing model with habit formation (Forthcoming in Asia-Pacific Financial Markets)

Author

Listed:
  • Masaaki Fujii

    (Quantitative Finance Course, Graduate School of Economics, The University of Tokyo)

  • Masashi Sekine

    (Ph.D. Student at Quantitative Finance Course, 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 (Forthcoming in Asia-Pacific Financial Markets)," CARF F-Series CARF-F-587, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2024.
    • Handle: RePEc:cfi:fseres:cf587
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    References listed on IDEAS

    as
    1. Gordan Žitković, 2012. "An example of a stochastic equilibrium with incomplete markets," Finance and Stochastics, Springer, vol. 16(2), pages 177-206, April.
    2. 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.
    3. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    4. 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.
    5. 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.
    6. 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.
    7. Peter O. Christensen & Kasper Larsen, 2014. "Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 4(2), pages 247-285.
    8. Medvegyev, Peter, 2007. "Stochastic Integration Theory," OUP Catalogue, Oxford University Press, number 9780199215256.
    9. Detemple, Jerome B & Zapatero, Fernando, 1991. "Asset Prices in an Exchange Economy with Habit Formation," Econometrica, Econometric Society, vol. 59(6), pages 1633-1657, November.
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    11. Back, Kerry E., 2017. "Asset Pricing and Portfolio Choice Theory," OUP Catalogue, Oxford University Press, number 9780190241148.
    12. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457.
    13. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," Papers 2304.07108, arXiv.org, revised Oct 2023.
    14. Pollak, Robert A, 1970. "Habit Formation and Dynamic Demand Functions," Journal of Political Economy, University of Chicago Press, vol. 78(4), pages 745-763, Part I Ju.
    15. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.
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