SIMPOL Model for Solving Continuous-Time Heterogeneous Agent Problems

Battle Count: 64

The paper is primarily focused on macroeconomic modeling of heterogeneous agents (wealth distribution, consumption-savings decisions). While the underlying stochastic control framework (HJB equations, diffusion processes) shares mathematical foundations with portfolio optimization and derivative pricing, the paper does not address trading strategies, market microstructure, or asset pricing directly. The Merton model validation is tangentially relevant to portfolio theory, but the application domain is macroeconomics rather than quantitative trading.

The core algorithm (Howard's policy iteration + upwind finite differences) is well-established and conceptually straightforward for a single PDE. However, the full SIMPOL framework involves: (1) coupled HJB-FPK system, (2) policy post-processing with smoothing and slope-band projection, (3) multiple diagnostic modules (Wasserstein-2 simulation, Merton validation, M-matrix checks), and (4) careful handling of boundary conditions and state constraints. The modular architecture reduces complexity per component, but integrating all pieces and tuning parameters (tolerances, grid size, smoothing steps) requires numerical expertise.

Full implementation openly available on Zenodo (DOI: 10.5281/zenodo.17216748). All parameters, grid settings, tolerances, and algorithmic steps are explicitly documented. Modular architecture allows independent verification of each component. Validation against known analytical solutions (Merton model) provides external benchmarking.