Mean-field Equilibrium Price Formation with Exponential Utility

Masaaki Fujii and Masashi Sekine
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Masaaki Fujii: Faculty of Economics, The University of Tokyo
Masashi Sekine: Faculty of Economics, The University of Tokyo

No CIRJE-F-1210, CIRJE F-Series from CIRJE, Faculty of Economics, 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 pages
Date: 2023-04
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2023cf1210

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