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A trajectorial interpretation of Doob's martingale inequalities

Acciaio, B., Beigelböck, M., Penkner, F., Schachermayer, W. and Temme, J. (2013) A trajectorial interpretation of Doob's martingale inequalities. Annals of Applied Probability, 23 (4). pp. 1494-1505. ISSN 1050-5164

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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
Official URL:
Additional Information: © 2013 Institute of Mathematical Statistics
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Statistics
Projects: FA506041, MA09-003, p21209
Funders: European Research Council, Vienna Science & Technology Fund, Austrian Science Fund
Date Deposited: 27 Jun 2013 15:26

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