# Universal approximation theorems for continuous functions of c\`adl\`ag paths and L\'evy-type signature models

@inproceedings{Cuchiero2022UniversalAT, title={Universal approximation theorems for continuous functions of c\`adl\`ag paths and L\'evy-type signature models}, author={Christa Cuchiero and Francesca Chiara Primavera and Sara Svaluto-Ferro}, year={2022} }

We prove two versions of a universal approximation theorem that allow to approximate continuous functions of c`adl`ag (rough) paths via linear functionals of their time-extended signature, one with respect to the Skorokhod J 1 -topology and the other one with respect to (a rough path version of) the Skorokhod M 1 -topology. Our main motivation to treat this question comes from signature-based models for ﬁnance that allow for the inclusion of jumps. Indeed, as an important application, we deﬁne…

## One Citation

### Signature-based models: theory and calibration

- Mathematics
- 2022

We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian…

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