Mean field equilibrium asset pricing model with habit formation

TL;DR

This paper develops a mean field game asset pricing model with habit formation, deriving a quadratic-growth BSDE to characterize equilibrium and providing a semi-analytic solution in an incomplete market with many heterogeneous agents.

Contribution

It introduces a novel mean field equilibrium asset pricing framework incorporating habit formation and solves it using a quadratic-growth BSDE and exponential quadratic Gaussian reformulation.

Findings

Derived a quadratic-growth mean field BSDE for equilibrium characterization.

Established well-posedness and asymptotic behavior of the model.

Provided a semi-analytic solution via exponential quadratic Gaussian reformulation.

Abstract

This paper presents an asset pricing model in an incomplete market involving a large number of heterogeneous agents based on the mean field game theory. In the model, we incorporate habit formation in consumption preferences, which has been widely used to explain various phenomena in financial economics. In order to characterize the market-clearing equilibrium, we derive a quadratic-growth mean field backward stochastic differential equation (BSDE) and study its well-posedness and asymptotic behavior in the large population limit. Additionally, we introduce an exponential quadratic Gaussian reformulation of the asset pricing model, in which the solution is obtained in a semi-analytic form.