On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales
Mathematical Finance
2022-02-15 v6 Probability
Abstract
We prove the existence and uniqueness of solutions of SDEs with Lipschitz coefficients, driven by continuous, model-free martingales. The main tool in our reasoning is Picard's iterative procedure and a model-free version of the Burkholder-Davis-Gundy inequality for integrals driven by model-free, continuous martingales. We work with a new outer measure which assigns zero value exactly to those properties which are instantly blockable.
Cite
@article{arxiv.1807.05692,
title = {On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales},
author = {Lesiba Ch. Galane and Rafał M. Łochowski and Farai J. Mhlanga},
journal= {arXiv preprint arXiv:1807.05692},
year = {2022}
}