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

Yves Achdou and Qing Tang ()
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Yves Achdou: LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité
Qing Tang: CUG - China University of Geosciences [Wuhan]

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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.

Keywords: Hamilton-Jacobi-Bellman equation Mean Field Games recursive utility finite difference iterative algorithms; Hamilton-Jacobi-Bellman equation; Mean Field Games; recursive utility; finite difference; iterative algorithms (search for similar items in EconPapers)
Date: 2026
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