Analysis and Probability Seminar
A trajectorial interpretation of Doob's martingale inequalities
Walter Schachermayer (University of Vienna)
Friday, October 12, 2018
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. Based on the joint work with Acciaio, Bieglbock, Penkner, and Temme.