A TRAJECTORIAL INTERPRETATION OF DOOB'S MARTINGALE INEQUALITIES

• 成果类型: Article
• 署名作者: Acciaio, B.; Beiglboeck, M.; Penkner, F.; Schachermayer, W.; Temme, J.
• 署名单位: University of Vienna; University of Perugia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP878
• 发表日期: 2013
• 页码: 1494-1505
• 关键词: log l-inequality; stochastic integration; littlewood; hardy

摘要

We present a unified approach to Doob's L-p maximal inequalities for 1 <= p < infinity. 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.