Mean Field Equilibrium Asset Pricing Models With Exponential Utility

TL;DR

This thesis develops mean field equilibrium asset pricing models with heterogeneous agents and exponential utility, using novel mean field BSDEs, and extends to consumption, habit formation, and partially observable markets.

Contribution

Introduces a new mean field BSDE framework for equilibrium asset pricing with exponential utility and heterogeneity, including extensions to consumption, habit formation, and partial observability.

Findings

Existence of solutions to the mean field BSDEs with quadratic growth.

Market clearing risk premium in large populations.

Semi-analytic solutions via exponential quadratic Gaussian reformulation.

Abstract

This thesis develops equilibrium asset pricing models in incomplete markets with a large number of heterogeneous agents using mean field game theory. The market equilibrium is characterized by a novel form of mean field backward stochastic differential equations (BSDEs). First, we propose a theoretical model that endogenously derives the equilibrium risk premium. Agents with exponential preferences are heterogeneous in initial wealth, risk aversion, and unspanned stochastic terminal liability. We solve the optimal investment problem using the optimal martingale principle. The equilibrium is characterized by a mean field BSDE whose driver has quadratic growth in both the stochastic integrands and their conditional expectations. We prove the existence of solutions and show that the risk premium clears the market in the large population limit. Second, we extend the model to include consumption and habit formation, relaxing the time-separability assumption of utility functions. A similar mean field BSDE is derived, and its well-posedness and asymptotic behavior are examined. We also introduce an exponential quadratic Gaussian (EQG) reformulation to obtain equilibrium solutions in semi-analytic form. Finally, the model is extended to partially observable markets where agents must infer the risk premium from stock price observations to determine trading strategies. We provide semi-analytic expressions for the equilibrium via the EQG framework, and the equilibrium risk-premium process is constructed endogenously using Kalman-Bucy filtering theory. Numerical simulations are included to visualize the resulting market dynamics.