A trajectorial interpretation of Doob's martingale inequalities
Acciaio, B., Beigelböck, M., Penkner, F., Schachermayer, W. & Temme, J.
(2013).
A trajectorial interpretation of Doob's martingale inequalities.
Annals of Applied Probability,
23(4), 1494-1505.
https://doi.org/10.1214/12-AAP878
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.
| Item Type | Article |
|---|---|
| Copyright holders | © 2013 Institute of Mathematical Statistics |
| Departments | LSE > Academic Departments > Statistics |
| DOI | 10.1214/12-AAP878 |
| Date Deposited | 27 Jun 2013 |
| URI | https://researchonline.lse.ac.uk/id/eprint/50116 |
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- https://www.scopus.com/pages/publications/84879776764 (Scopus publication)
- http://www.imstat.org/aap (Official URL)