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), Artificial Intelligence and the Macroeconomy Conference (2026)

(*by co-author)

Entrepreneurial Risk Sharing, Subjective Return Uncertainty, and Inefficient Wealth Inequality

Abstract: I study how heterogeneity in entrepreneurs' equity financing opportunities and in households’ belief precision about public equity returns as the opportunity cost of entrepreneurial self-financing affect aggregate efficiency and wealth inequality. First, I document that U.S. entrepreneurs face substantial uninsurable risk: about 40% of their financial and business wealth is invested in their main firm’s equity. Furthermore, wealthier entrepreneurs retain ownership at lower, but bounded, shares and are therefore less constrained in raising capital from and sharing risk with outside investors. I interpret these facts using a model of entrepreneurship with incomplete markets and financial frictions, showing that wealth-dependent financing constraints and risk-sharing opportunities generate additional productivity losses. Second, I show that the wealthiest 20% of U.S. households perceive lower subjective uncertainty about diversified equity returns than the bottom 80%. Incorporating heterogeneity in belief precision about the opportunity cost of self-financing allows me to study its implications for entrepreneurial activity and inequality. Calibrating the model to household microdata, I quantify implications for the efficient taxation of entrepreneurial capital.

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)