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

Author

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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])

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.

Suggested Citation

  • Yves Achdou & Qing Tang, 2026. "Finite difference methods for a continuous-time heterogeneous agent model with recursive utility," Working Papers hal-05666966, HAL.
    • Handle: RePEc:hal:wpaper:hal-05666966
    Note: View the original document on HAL open archive server: https://hal.science/hal-05666966v1
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