PreprintCC BY 4.0arXiv
On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations
Abstract
We establish first- and second-order Pontryagin (a.k.a. stochastic) maximum principles for rough stochastic control problems with general nonlinear Lipγ-rough vector fields. This complements the dynamic programming approach of Friz-Lê-Zhang [FLZ26b], and extends the maximum principle of Horst-Zhang [HZ26] beyond affine rough vector fields. The paper concludes with applications to pathwise stochastic optimal control.
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BibTeX
@misc{friz2026pontryagin,
title = {{On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations}},
author = {Peter K. Friz and Ulrich Horst and Stefanos Theodorakopoulos and Huilin Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36653},
eprint = {2610.36653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36653},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations
AU - Peter K. Friz
AU - Ulrich Horst
AU - Stefanos Theodorakopoulos
AU - Huilin Zhang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36653
UR - https://arxiv.org/abs/2610.36653
AB - We establish first- and second-order Pontryagin (a.k.a. stochastic) maximum principles for rough stochastic control problems with general nonlinear Lip^γ-rough vector fields. This complements the dynamic programming approach of Friz-Lê-Zhang [FLZ26b], and extends the maximum principle of Horst-Zhang [HZ26] beyond affine rough vector fields. The paper concludes with applications to pathwise stochastic optimal control.
ER -