Mean-field equilibrium price formation with exponential utility

Masaaki Fujii and Masashi Sekine
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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.

No CARF-F-594, CARF F-Series from Center for Advanced Research in Finance, Faculty 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.

Pages: 31
Date: 2023-10, Revised 2025-01
New Economics Papers: this item is included in nep-gth and nep-upt
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