Mean field equilibrium asset pricing model under partial observation: An exponential quadratic Gaussian approach

TL;DR

This paper develops a mean field equilibrium asset pricing model for markets with partial observation, utilizing an exponential quadratic Gaussian approach and Kalman-Bucy filtering to infer unobservable risk premiums.

Contribution

It introduces a semi-analytical solution to the mean field BSDE for the risk premium using an exponential quadratic Gaussian framework, incorporating filtering techniques.

Findings

Derived a semi-analytical expression for the equilibrium risk premium.

Implemented Kalman-Bucy filtering to estimate unobservable risk premiums.

Provided numerical simulations illustrating market dynamics under partial observation.

Abstract

This paper studies an asset pricing model in a partially observable market with a large number of heterogeneous agents using the mean field game theory. In this model, we assume that investors can only observe stock prices and must infer the risk premium from these observations when determining trading strategies. We characterize the equilibrium risk premium in such a market through a solution to the mean field backward stochastic differential equation (BSDE). Specifically, the solution to the mean field BSDE can be expressed semi-analytically by employing an exponential quadratic Gaussian framework. We then construct the risk premium process, which cannot be observed directly by investors, endogenously using the Kalman-Bucy filtering theory. In addition, we include a simple numerical simulation to visualize the dynamics of our market model.