Solving Heterogeneous agent models in Continuous Time with Adaptive Sparse Grids

Du, Zaichuan (2026): Solving Heterogeneous agent models in Continuous Time with Adaptive Sparse Grids.

Abstract

This paper proposes a new approach to numerically solving a wide class of heterogeneous agent models in continuous time using adaptive sparse grids. I combine the sparse finite difference method with the sparse finite volume method to solve the Hamilton-Jacobian-Bellman equation and Kolmogorov Forward equation, respectively, within an implicit Cartisian Discrete Exterior Calculus (DEC) super-mesh. My algorithm automatically adapts grids and adds local resolutions in regions of the state space where both the value function and the distribution approximation errors remains large. The algorithm is asymptotically convergent guaranteed by the Petrov-Galerkin projection. I demonstrate the power of my approach in applications featuring high-dimensional state spaces, occasionally binding constraints, lifecycle and overlapping generations.

• Item Type: MPRA Paper
• Language: English
• Keywords: heterogeneous agent, continuous time, adaptive sparse grids, occasionally binding constraints, overlapping generation, lifecycle
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth

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