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

TL;DR

This paper establishes existence and uniqueness of solutions for stochastic differential equations with Lipschitz coefficients driven by continuous, model-free martingales, using a novel outer measure and iterative methods.

Contribution

It introduces a model-free framework for SDEs driven by continuous martingales, extending classical results to a new setting with a new outer measure.

Findings

Proves existence and uniqueness of solutions for the SDEs.

Develops a model-free Burkholder-Davis-Gundy inequality.

Introduces a new outer measure for analyzing properties.

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.