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Mean-field equilibrium price formation with exponential utility

Author

Listed:
  • Masaaki Fujii

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

  • Masashi Sekine

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

Abstract

In this paper, using the mean-field game theory, we study a problem of equilibrium price formation among many investors with exponential utility in the presence of liabilities unspanned by the security prices. The investors are heterogeneous in their initial wealth, risk-averseness parameter, as well as stochastic liability at the terminal time. We characterize the equilibrium risk-premium process of the risky stocks in terms of the solution to a novel mean-field backward stochastic differential equation (BSDE), whose driver has quadratic growth both in the stochastic integrands and in their conditional expectations. We prove the existence of a solution to the mean-field BSDE under several conditions and show that the resultant risk-premium process actually clears the market in the large population limit.

Suggested Citation

  • Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," CARF F-Series CARF-F-594, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2025.
    • Handle: RePEc:cfi:fseres:cf594
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    References listed on IDEAS

    as
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    4. Back, Kerry E., 2017. "Asset Pricing and Portfolio Choice Theory," OUP Catalogue, Oxford University Press, number 9780190241148.
    5. Masaaki Fujii & Akihiko Takahashi, 2015. "Quadratic-exponential growth BSDEs with Jumps and their Malliavin's Differentiability," Papers 1512.05924, arXiv.org, revised Sep 2017.
    6. Hao Xing, 2017. "Consumption–investment optimization with Epstein–Zin utility in incomplete markets," Finance and Stochastics, Springer, vol. 21(1), pages 227-262, January.
    7. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
    8. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
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