Work

On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.36653

Authors: Friz, Peter K., Horst, Ulrich, Theodorakopoulos, Stefanos, Zhang, Huilin

Institutions: Weierstrass Institute for Applied Analysis and Stochastics, Technische Universität Berlin, Humboldt-Universität zu Berlin, Shandong University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: National Science Foundation, Deutsche Forschungsgemeinschaft, Fundamental Research Funds for the Central Universities

Awards: G5709080070, G7650316851

OpenAlex ID: W7224107782

Cites:

Cited by:

Related to: 10