Stability of the Weak Martingale Optimal Transport Problem
Probability
2022-04-05 v2 Mathematical Finance
Abstract
While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also non-linear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali this corresponds to weak martingale optimal transport (WMOT). In this article we establish stability of WMOT which is important since financial data can give only imprecise information on the underlying marginals. As application, we deduce the stability of the superreplication bound for VIX futures as well as the stability of stretched Brownian motion and we derive a monotonicity principle for WMOT.
Cite
@article{arxiv.2109.06322,
title = {Stability of the Weak Martingale Optimal Transport Problem},
author = {Mathias Beiglböck and Benjamin Jourdain and William Margheriti and Gudmund Pammer},
journal= {arXiv preprint arXiv:2109.06322},
year = {2022}
}