Stability of a Heterogeneous Agent Model with Precautionary Savings

朱胜豪，现任对外经济贸易大学教授。纽约大学经济学博士。在Econometrica, Journal of Economic Theory, International Economic Review等国际一流经济学期刊上发表数篇论文。学术成果在Google Scholar上被国际同行引用1000多次。朱胜豪教授的主要研究领域是宏观经济和收入分配。他的研究结合动态宏观经济学异质性模型和家庭微观大数据，利用计算技术解决微观主体决策的激励相容问题。正在主持一项国家自然科学基金原创探索计划项目。 

The continuous-time heterogeneous-agent formulated by Achdou–Han–Lasry–Lions–Moll (2022) turns an individual Hamilton–Jacobi equation and a population Kolmogorov equation into a backward–forward PDE system. The individual wealth accumulation under the Macro general equilibrium follows a McKean-Valsov stochastic differential equation. We find that the wealth distribution converges to a stationary distribution within a ball characterized by the relative entropy. We establish the local stability of the macroeconomy modeled as a nonlinear particle system. Finally, leveraging the relationship between Dirichlet forms and KL divergence, we investigate the stability of heterogeneous macroeconomic models via functional inequality techniques.