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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{achdou2026finite,
  title = {{Finite difference methods for a continuous-time heterogeneous agent model with recursive utility}},
  author = {Yves Achdou and Qing Tang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.23408},
  eprint = {2606.23408},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.23408},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Finite difference methods for a continuous-time heterogeneous agent model with recursive utility
AU  - Yves Achdou
AU  - Qing Tang
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2606.23408
UR  - https://arxiv.org/abs/2606.23408
AB  - 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.
ER  -