Research

A Global Solution Method for HACT Models with Aggregate Risk with Elisabeth Pröhl*

Abstract: Heterogeneous agent models in continuous time (HACT) have become a workhorse in macroeconomics, but incorporating aggregate risk remains a major computational challenge. Existing methods often rely on local approximations or restrict models to quasi-stationary settings, limiting their ability to capture nonlinear macroeconomic dynamics. This paper introduces a novel approach that globally solves HACT models with aggregate risk by leveraging the master equation. Our approach transforms this non-standard partial differential equation (PDE) into a high-dimensional yet standard PDE using Polynomial Chaos expansions, enabling the application of advanced but off-the-shelf deep learning techniques from the applied mathematics literature. Specifically, we adapt the Deep BSDE method to solve this equation efficiently. To demonstrate its applicability, we solve a two-asset HACT model with aggregate risk featuring adjustment costs and collateral constraints. By overcoming a key computational barrier, our method enables the study of fully nonlinear heterogeneous agent models, opening new avenues for macroeconomic research.

Presentations: T2M Conference (2025), Centre for Advanced Study at the Norwegian Academy of Science and Letters (2025), ECONDAT Conference (2025), Stanford Institute for Theoretical Economics: Models, Solution Methods, and Applications (2025)*, World Congress of the Econometric Society (2025)* (*by co-author)

Non-homothetic Habit Formation, Wealth Inequality and the Equity Premium

Abstract: Understanding why the growth in wealth is even more unequally distributed than wealth itself remains a fundamental challenge in macro-finance. This paper introduces endogenous subsistence consumption as a novel micro-foundation for return heterogeneity and non-homothetic preferences as pivotal model assumptions generating the observed inequality in consumption, income, wealth, and capital income. To study whether the general-equilibrium effects of subsistence consumption reinforce a scale-dependence in wealth returns, I develop an analytical representation of endogenous asset returns in terms of the distribution of households' consumption-portfolio choices. This representation can replace implicit market-clearing conditions complicating numerical solution methods for heterogeneous agent models with aggregate risk. By combining martingale pricing with a mean-field approach, this provides new insights as well as a useful tool for the inquiry into mechanisms driving wealth inequality.

Presentations: Research in Behavioral Finance Conference (2024), 11th ECINEQ Conference (2025)