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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
    1. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
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    3. Back, Kerry E., 2017. "Asset Pricing and Portfolio Choice Theory," OUP Catalogue, Oxford University Press, number 9780190241148.
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    5. Hao Xing, 2017. "Consumption–investment optimization with Epstein–Zin utility in incomplete markets," Finance and Stochastics, Springer, vol. 21(1), pages 227-262, January.
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    7. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
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