On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations

We establish first- and second-order Pontryagin (a.k.a. stochastic) maximum principles for rough stochastic control problems with general nonlinear $\mathrm{Lip}^γ$-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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.36653
Primary Topic
Stochastic processes and financial applications
Type
preprint
Controls
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preprint

On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations

Ulrich Horst, Stefanos Theodorakopoulos, Peter K. Friz, Huilin Zhang
arXiv (Cornell University)
Stochastic processes and financial applications
preprint

On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations

Ulrich Horst, Stefanos Theodorakopoulos, Peter K. Friz, Huilin Zhang
preprint en

Abstract

We establish first- and second-order Pontryagin (a.k.a. stochastic) maximum principles for rough stochastic control problems with general nonlinear $\mathrm{Lip}^γ$-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.

arXiv (Cornell University)
Stochastic processes and financial applications
DOIOpen Access PDFOpenAlex
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On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations — Ulrich Horst, Stefanos Theodorakopoulos, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS