Martingale Inequalities and Deterministic Counterparts
Probability
2014-10-21 v2 Pricing of Securities
Abstract
We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the martingale inequality is determined by a fixed point of a simple nonlinear operator involving a concave envelope. Our results yield an explanation for certain inequalities that arise in mathematical finance in the context of robust hedging.
Cite
@article{arxiv.1401.4698,
title = {Martingale Inequalities and Deterministic Counterparts},
author = {Mathias Beiglböck and Marcel Nutz},
journal= {arXiv preprint arXiv:1401.4698},
year = {2014}
}
Comments
22 pages