Martingale inequalities for the maximum via pathwise arguments

Jan Obłój, Peter Spoida, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


We study a class of martingale inequalities involving the running max- imum process. They are derived from pathwise inequalities introduced by Henry- Labordère et al. (Ann. Appl. Probab., 2015 [arxiv:1203.6877v3]) and provide an upper bound on the expectation of a function of the running maximum in terms of marginal distributions at n intermediate time points. The class of inequalities is rich and we show that in general no inequality is uniformly sharp—for any two inequalities we specify martingales such that one or the other inequality is sharper. We use our inequalities to recover Doob’s Lp inequalities. Further, for p = 1 we refine the known inequality and for p < 1 we obtain new inequalities.

Original languageEnglish (US)
Pages (from-to)227-247
Number of pages21
JournalLecture Notes in Mathematics
StatePublished - 2015

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Martingale inequalities for the maximum via pathwise arguments'. Together they form a unique fingerprint.

Cite this