From optimal stopping boundaries to Rost's reversed barriers and the Skorokhod embedding

Tiziano De Angelis

Published 2015-05-11Version 1

We investigate the connection between Rost's solution of the Skorokhod embedding problem and a suitable family of optimal stopping problems for Brownian motion with finite time-horizon. In particular we prove by probabilistic methods and stochastic calculus that the time reversal of the optimal stopping sets for such problems form the so-called Rost's reversed barrier.