On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales

Lesiba Ch. Galane, Rafa{\l} M. {\L}ochowski and Farai J. Mhlanga

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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.

Date: 2018-07, Revised 2022-02
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