{"ID":2864070,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23557","arxiv_id":"2509.23557","title":"SIMPOL Model for Solving Continuous-Time Heterogeneous Agent Problems","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.","short_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 H...","url_abs":"https://arxiv.org/abs/2509.23557","url_pdf":"https://arxiv.org/pdf/2509.23557v1","authors":"[\"Ricardo Alonzo Fernández Salguero\"]","published":"2025-09-28T01:37:29Z","proceeding":"q-fin.CP","tasks":"[\"q-fin.CP\",\"cs.MA\",\"econ.TH\"]","methods":"[\"Large Language Model\"]","has_code":false}