English

A trajectorial interpretation of Doob's martingale inequalities

Probability 2013-07-22 v4 General Finance

Abstract

We present a unified approach to Doob's LpL^p maximal inequalities for 1p<1\leq p<\infty. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging. Moreover, our deterministic inequalities lead to new versions of Doob's maximal inequalities. These are best possible in the sense that equality is attained by properly chosen martingales.

Keywords

Cite

@article{arxiv.1202.0447,
  title  = {A trajectorial interpretation of Doob's martingale inequalities},
  author = {B. Acciaio and M. Beiglböck and F. Penkner and W. Schachermayer and J. Temme},
  journal= {arXiv preprint arXiv:1202.0447},
  year   = {2013}
}

Comments

Published in at http://dx.doi.org/10.1214/12-AAP878 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)