## The Annals of Applied Probability

### A trajectorial interpretation of Doob’s martingale inequalities

#### Abstract

We present a unified approach to Doob’s $L^{p}$ maximal inequalities for $1\leq p<\infty$. 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.

#### Article information

Source
Ann. Appl. Probab., Volume 23, Number 4 (2013), 1494-1505.

Dates
First available in Project Euclid: 21 June 2013

https://projecteuclid.org/euclid.aoap/1371834036

Digital Object Identifier
doi:10.1214/12-AAP878

Mathematical Reviews number (MathSciNet)
MR3098440

Zentralblatt MATH identifier
1274.60136

#### Citation

Acciaio, B.; Beiglböck, M.; Penkner, F.; Schachermayer, W.; Temme, J. A trajectorial interpretation of Doob’s martingale inequalities. Ann. Appl. Probab. 23 (2013), no. 4, 1494--1505. doi:10.1214/12-AAP878. https://projecteuclid.org/euclid.aoap/1371834036

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