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), CEF Conference (2026)*, SED Annual Meeting (2026)*

(*by co-author)

Entrepreneurial Risk, Return Uncertainty, and Wealth Inequality

Abstract: I study how heterogeneity in beliefs about diversified equity returns -- the opportunity cost of entrepreneurial self-financing -- affects aggregate efficiency and wealth inequality. I first document that U.S. entrepreneurs allocate substantial wealth to both their own firms and publicly traded assets: equity in their largest firm accounts for approximately 40\% of financial and business wealth on average. I interpret this portfolio allocation in a model of financially constrained entrepreneurs, where uninsurable business risk creates a tradeoff between entrepreneurial investment and diversification. Heterogeneity in endogenous risk-bearing capacity generates aggregate productivity losses beyond those arising from credit constraints. Second, I show that subjective uncertainty about the distribution of diversified equity returns varies systematically across households: self-employed household heads and the wealthiest 20% are significantly less uncertain than salaried workers and the bottom 80% respectively. Incorporating occupational choice under heterogeneous belief precision at both margins, the model predicts that greater uncertainty about outside investment opportunities can increase entrepreneurial entry, consistent with state-level evidence from Kauffman entrepreneurship indicators. Calibrating the model to household microdata, I quantify the implications for the efficient taxation of entrepreneurial capital.

Presentations: CESifo Area Conference on Macro with Micro Data (2026), BSE Summer Forum: Inequality and Effiency (2026), CEF Conference (2026)

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)