Heterogeneous-Agent Asset Pricing with the Master Equation: Idiosyncratic Risk in a Production Economy with Habit Formation

Uninsurable income risk is a long-considered driver of risk premia and wealth inequality. This paper augments idiosyncratic risk with internal and external habit formation seeking to explain the equity premium and observed heterogeneity in household portfolios. I develop a local solution method to solve for equilibrium returns and the distribution of portfolio allocations in a stochastic production economy. By explicitly treating the cross-sectional distribution of households as a state variable, I combine martingale pricing with mean-field-games methods to characterize equilibrium as the solution to the ‘Master Equation’. Perturbing this equation offers a novel approach to heterogeneous-agent asset pricing in settings with rich distribution-dependencies.