Niklas Bonnmann

Work in progress

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

Abstract: We develop a method to compute global solutions to continuous-time heterogeneous agent (HACT) models with aggregate risk, non-stationarity, and financial constraints. When the cross-sectional distribution evolves stochastically, the associated master equation becomes second order. First, we provide a heuristic derivation of the second-order master equation with a stochastic Kolmogorov forward equation and show how its distributional derivatives can be approximated using a polynomial chaos expansion, thereby transforming it into a standard, albeit high-dimensional, partial differential equation (PDE). Second, building on the Deep BSDE approach for high-dimensional PDEs, we develop a general-equilibrium extension -- GE-Deep BSDE -- that jointly solves for value functions, equilibrium prices, and distributional consistency using multi-objective deep learning. Applying the method to a two-asset model, we show that while total factor productivity shocks fail to generate sufficient risk premia, stochastic capital depreciation with collateral constraints produces endogenous risk and helps reconcile microeconomic wealth dispersion with macro-finance evidence.

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 the wealthiest 20\% of U.S. households perceive aggregate equity return uncertainty to be significantly lower  than the bottom-80\%. I interpret this as evidence for persistent informational inequality. To quantify its contribution to the observed heterogeneity in wealth returns, I develop a heterogeneous-agent model with portfolio choice and frictional learning. The precision of households’ return expectations varies both due to heterogeneous skills (type-effects) and due to pecuniary information costs (scale-effects). In contrast to utility-costs, the latter give rise to a first-order wealth dependence in information acquisition, generating scale-effects through a feedback between information and wealth accumulation. Type-effects on the other hand may induce distinct precautionary-saving motives. A joint calibration strategy targeting both types of frictions allows me to analyze their joint implications for inequality and the insurance-efficiency trade-off in taxing wealth or 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)