Work

Functional differential equations driven by càdlàg rough paths

Year: 2025

Type: article

Abstract: The existence of unique solutions is established for rough differential equations (RDEs) with path-dependent coefficients and driven by càdlàg rough paths. Moreover, it is shown that the associated solution map, also known as Itô–Lyons map, is locally Lipschitz continuous. These results are then applied to various classes of rough differential equations, such as controlled RDEs and RDEs with delay, as well as to stochastic differential equations with delay. To that end, a joint rough path is constructed for a càdlàg martingale and its delayed version, that corresponds to stochastic Itô integration.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1381

Authors: Anna P. Kwossek, Andreas Neuenkirch, David J. Prömel

Institutions: University of Vienna, University of Mannheim

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Baden-Württemberg Stiftung, Universität Mannheim