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PreprintarXiv licencearXiv

Backward SDE characterization of the finite horizon Principal-Agent problem

  • Yuxing Huang
  • Nizar Touzi
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Abstract

We consider the finite horizon continuous-time Principal--Agent problem under deterministic discount factors. Following the Sannikov reduction to a stochastic control problem, we provide a further characterization of the Principal's value function in terms of a backward SDE inducing the corresponding optimal contract. In particular, this allows to bypass the fully nonlinear HJB equation satisfied by the Principal value function in the Markovian setting. This new approach allows to handle a new class of Principal-Agent problems which was not accessible with the existing method, namely the setting where the Agent faces a regime-switching control problem.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026backward,
  title = {{Backward SDE characterization of the finite horizon Principal-Agent problem}},
  author = {Yuxing Huang and Nizar Touzi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.22818},
  eprint = {2608.22818},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.22818},
}
RIS
TY  - UNPB
TI  - Backward SDE characterization of the finite horizon Principal-Agent problem
AU  - Yuxing Huang
AU  - Nizar Touzi
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2608.22818
UR  - https://arxiv.org/abs/2608.22818
AB  - We consider the finite horizon continuous-time Principal--Agent problem under deterministic discount factors. Following the Sannikov reduction to a stochastic control problem, we provide a further characterization of the Principal's value function in terms of a backward SDE inducing the corresponding optimal contract. In particular, this allows to bypass the fully nonlinear HJB equation satisfied by the Principal value function in the Markovian setting. This new approach allows to handle a new class of Principal-Agent problems which was not accessible with the existing method, namely the setting where the Agent faces a regime-switching control problem.
ER  -