Year: 2026
Type: preprint
Abstract: We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients whose regularity is formulated in terms of horizontal and vertical Dupire derivatives. Under the same regularity assumptions as in Ananova~\cite{An23}, we develop a new causal Taylor argument and establish a second-order remainder estimate. This removes the regularity loss responsible for the restriction $2\leq p<1+\sqrt{2}$ in~\cite{An23} and extends the existence result to the full range $2\le p<3$.
Source: arXiv (Cornell University)
Authors: Gao, Xing, Li, Nannan
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Awards: G4388067730, G4828426884
OpenAlex ID: W7223404209