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PreprintCC BY 4.0arXiv

Comparison Principle and Semi-Lagrangian Methods for a Hamilton--Jacobi--Bellman System with Recursive Utility

  • Qing Tang
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Abstract

We consider a system of coupled first-order Hamilton--Jacobi--Bellman equations arising in continuous-time heterogeneous agent models with recursive utility, a class of models that has attracted increasing attention in macroeconomics. The first part of the paper establishes a comparison principle for the system when preferences exhibit early resolution of uncertainty. A key ingredient in the proof is an ordinally equivalent transformation of the recursive utility representation. In the second part, we develop semi-Lagrangian schemes and iterative algorithms for solving the associated nonlinear discrete systems. For preferences exhibiting late resolution of uncertainty, we establish a first-order error estimate for the semi-Lagrangian approximation. Numerical experiments demonstrate that the proposed methods yield results consistent with those obtained using the previously developed finite difference schemes.

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Cite

BibTeXRIS
BibTeX
@misc{tang2026comparison,
  title = {{Comparison Principle and Semi-Lagrangian Methods for a Hamilton--Jacobi--Bellman System with Recursive Utility}},
  author = {Qing Tang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02763},
  eprint = {2611.02763},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02763},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Comparison Principle and Semi-Lagrangian Methods for a Hamilton--Jacobi--Bellman System with Recursive Utility
AU  - Qing Tang
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02763
UR  - https://arxiv.org/abs/2611.02763
AB  - We consider a system of coupled first-order Hamilton--Jacobi--Bellman equations arising in continuous-time heterogeneous agent models with recursive utility, a class of models that has attracted increasing attention in macroeconomics. The first part of the paper establishes a comparison principle for the system when preferences exhibit early resolution of uncertainty. A key ingredient in the proof is an ordinally equivalent transformation of the recursive utility representation. In the second part, we develop semi-Lagrangian schemes and iterative algorithms for solving the associated nonlinear discrete systems. For preferences exhibiting late resolution of uncertainty, we establish a first-order error estimate for the semi-Lagrangian approximation. Numerical experiments demonstrate that the proposed methods yield results consistent with those obtained using the previously developed finite difference schemes.
ER  -