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Peer-reviewedCC BY 4.0PLOS One

Iterative spectral methods for Hamilton-Jacobi-Bellman quasi-variational inequality in finance

  • Minlan Lei1
  • Zhengyang Lu
  1. 1School of Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan, China
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Abstract

This study proposes a novel computational scheme for utility-maximization problems involving optimal stopping, formulated as Hamilton-Jacobi-Bellman quasi-variational inequalities. The methodology integrates Gauss-Lobatto-Legendre spectral discretization with a penalization method and is solved efficiently via policy iteration. We establish the convergence of the penalized scheme and verify the effectiveness and robustness of the framework through a series of numerical experiments.

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Cite

BibTeXRIS
BibTeX
@article{lei2026iterative,
  title = {{Iterative spectral methods for Hamilton-Jacobi-Bellman quasi-variational inequality in finance}},
  author = {Minlan Lei and Zhengyang Lu},
  journal = {PLOS One},
  year = {2026},
  month = sep,
  doi = {10.1371/journal.pone.0359303},
  url = {https://doi.org/10.1371/journal.pone.0359303},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Iterative spectral methods for Hamilton-Jacobi-Bellman quasi-variational inequality in finance
AU  - Minlan Lei
AU  - Zhengyang Lu
PY  - 2026
DA  - 2026/09/30
JO  - PLOS One
DO  - 10.1371/journal.pone.0359303
UR  - https://doi.org/10.1371/journal.pone.0359303
AB  - This study proposes a novel computational scheme for utility-maximization problems involving optimal stopping, formulated as Hamilton-Jacobi-Bellman quasi-variational inequalities. The methodology integrates Gauss-Lobatto-Legendre spectral discretization with a penalization method and is solved efficiently via policy iteration. We establish the convergence of the penalized scheme and verify the effectiveness and robustness of the framework through a series of numerical experiments.
SN  - 1932-6203
ER  -