A trajectorial interpretation of Doob's martingale inequalities

By Beatrice Acciaio, Mathias Beiglböck, Friedrich Penkner, Walter Schachermayer, Johannes Temme. 2012

54 citations recorded by the source corpus.

We present a unified approach to Doob’s Lp maximal inequalities for 1 ≤ p < 1. 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.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/51ce90c898dc3928f3247e6c8db44d6e9e04b7f8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Nizar Touzi
2. Mathias Beiglbock
3. H. M. Soner
4. Martin Huesmann
5. Yan Dolinsky
6. Pierre Henry-Labordère
7. Peter Spoida
8. Alexander M. G. Cox

In Finance

1. Nizar Touzi
2. Mathias Beiglbock
3. Marcel Nutz
4. H. M. Soner
5. Yan Dolinsky
6. Martin Huesmann
7. Pierre Henry-Labordère
8. Alexander M. G. Cox

In Mathematical Physics

1. Nizar Touzi
2. Mathias Beiglbock
3. H. M. Soner
4. Yan Dolinsky
5. Pierre Henry-Labordère
6. Peter Spoida
7. Alexander M. G. Cox
8. Jan Obłój

Citations in the corpus

• Optimal transport and Skorokhod embedding (2013, background): “For the general case we recall the pathwise version of Doob’s inequality (see [1])”
• The maximum maximum of a martingale with given $\mathbf{n}$ marginals (2012, background): “A proof of one technical lemma is relegated to the Appendix.”
• Martingale optimal transport in the Skorokhod space (2014, background): “1 in [1] to conclude that for any k = 0, 1, .”