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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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    References listed on IDEAS

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    1. Achdou, Yves & Han, Jiequn & Lasry, Jean Michel & Lions, Pierre Louis & Moll, Ben, 2022. "Income and wealth distribution in macroeconomics: a continuous-time approach," LSE Research Online Documents on Economics 107422, London School of Economics and Political Science, LSE Library.
    2. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
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    6. Yuhki Hosoya, 2022. "On the Fragility of the Basis on the Hamilton-Jacobi-Bellman Equation in Economic Dynamics," Papers 2203.10595, arXiv.org, revised Jan 2024.
    7. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    8. Sethi, Suresh P. & Taksar, Michael, 1988. "A note on Merton's "Optimum Consumption and Portfolio Rules in a continuous-Time Model"," Journal of Economic Theory, Elsevier, vol. 46(2), pages 395-401, December.
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    10. Schesch, Constantin, 2024. "Pseudospectral methods for continuous-time heterogeneous-agent models," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
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