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SIMPOL Model for Solving Continuous-Time Heterogeneous Agent Problems

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  • Ricardo Alonzo Fern'andez Salguero

Abstract

This paper presents SIMPOL (Simplified Policy Iteration), a modular numerical framework for solving continuous-time heterogeneous agent models. The core economic problem, the optimization of consumption and savings under idiosyncratic uncertainty, is formulated as a coupled system of partial differential equations: a Hamilton-Jacobi-Bellman (HJB) equation for the agent's optimal policy and a Fokker-Planck-Kolmogorov (FPK) equation for the stationary wealth distribution. SIMPOL addresses this system using Howard's policy iteration with an *upwind* finite difference scheme that guarantees stability. A distinctive contribution is a novel consumption policy post-processing module that imposes regularity through smoothing and a projection onto an economically plausible slope band, improving convergence and model behavior. The robustness and accuracy of SIMPOL are validated through a set of integrated diagnostics, including verification of contraction in the Wasserstein-2 metric and comparison with the analytical solution of the Merton model in the no-volatility case. The framework is shown to be not only computationally efficient but also to produce solutions consistent with economic and mathematical theory, offering a reliable tool for research in quantitative macroeconomics.

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  • Ricardo Alonzo Fern'andez Salguero, 2025. "SIMPOL Model for Solving Continuous-Time Heterogeneous Agent Problems," Papers 2509.23557, arXiv.org.
    • Handle: RePEc:arx:papers:2509.23557
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    File URL: http://arxiv.org/pdf/2509.23557
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