Finite difference methods for a continuous-time heterogeneous agent model with recursive utility

Yves Achdou; Qing Tang

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arXiv · 2606.23408

Finite difference methods for a continuous-time heterogeneous agent model with recursive utility

Yves Achdou·Qing Tang

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Abstract

We propose, analyze and test computational methods for solving a continuous-time heterogenous agent model with Epstein-Zin utility. Such recursive utilities allow the model to disentangle between risk aversion and intertemporal substitution. Having discretized the Hamilton-Jacobi-Bellman (HJB) equation arising in the model, we propose a Howard-Newton algorithm for the late resolution preference case, and a Howard-Tarski-Kantorovich algorithm for the early resolution preference case. We prove the convergence of the iterative algorithms. We obtain as a consequence the existence of solutions to the discretized HJB equations. In the late resolution case, we supply a priori estimates between the unique solutions of the continuous and discretized HJB equations.

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Yves Achdou, Qing Tang. 2026-06-22. Finite difference methods for a continuous-time heterogeneous agent model with recursive utility. https://arxiv.org/abs/2606.23408

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