arXiv subjects

Lesiba Ch. Galane

Publications and source records attributed to Lesiba Ch. Galane.

2 recordsLinked to original sources

arXiv2022

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

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.

q-fin.MF↗

arXiv2018

On the quadratic variation of the model-free price paths with jumps

We prove that the model-free typical (in the sense of Vovk) càdlàg price paths with mildly restricted downward jumps possess quadratic variation which does not depend on the specific sequence of partitions as long as these partitions are obtained from stopping times such that the oscillations of a path on the consecutive (half-open on the right) intervals of these partitions tend (in a specified sense) to 0. Finally, we also define quasi-explicit, partition independent quantities which tend to this quadratic variation.

q-fin.MF↗