Niklas Bonnmann

Work in progress

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 stationary settings, limiting their ability to capture nonlinear macroeconomic dynamics. This paper introduces a novel approach that globally solves non-stationary HACT models with aggregate risk by leveraging the master equation. Our approach transforms this nonstandard 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 the master equation efficiently. To demonstrate its applicability, we not only solve a two-asset HACT model with aggregate risk featuring adjustment costs and collateral constraints but also its transition along a deterministic policy change.

Presentations: T2M Conference (2025), Centre for Advanced Study at the Norwegian Academy of Science and Letters (2025), ECONDAT Spring Meeting (2025), Stanford Institute for Theoretical Economics Workshop on Asset Pricing (2025)*, World Congress of the Econometric Society (2025)*, Conference on Deep Learning for Dynamic Stochastic Models (2025)

(*by co-author)

Wealth and Informational Inequality in Portfolio Choice

Abstract: Using data from the Survey of Consumer Expectations, I show that wealthier households generate more precise forecasts of the stock market Sharpe Ratio, reflecting lower perceived financial uncertainty even after controlling for observable characteristics. I interpret this as evidence of persistent informational inequality. To quantify its contribution to the observed wealth dependence in portfolio returns, I develop a heterogeneous-agent model with portfolio choice and frictional learning. The precision of households’ return expectations can vary both due to heterogeneous skills (type-effects) and due to information costs (scale-effects). I show that, to first order, pecuniary information costs generate a wealth-dependence in optimal information acquisition, while utility-based costs do not. Furthermore, I propose a calibration strategy that separates type- from scale-effects using my estimates of variation in forecast precision. This allows me to analyze how a realistic combination of both forms of informational frictions affects the insurance-efficiency trade-off in taxing wealth and capital income.

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), ECINEQ Conference (2025), INFER Annual Conference (2025), Econometric Society European Winter Meeting (2025)