@article{EJP3270,
author = {Mathias Beiglböck and Marcel Nutz},
title = {Martingale inequalities and deterministic counterparts},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Martingale inequality; Concave envelope; Fixed point; Robust hedging; Tchakaloff's theorem},
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.},
pages = {no. 94, 1-15},
issn = {1083-6489},
doi = {10.1214/EJP.v19-3270},
url = {http://ejp.ejpecp.org/article/view/3270}}