From optimal martingales to randomized dual optimal stopping

In this article we study and classify optimal martingales in the dual formulation of stopping problems. respect distinguish between weakly surely martingales. It is shown that family may be quite large. On other hand it Doob-martingale, is, martingale part Snell envelope, a certain sense robust under particular random perturbation. This new insight leads to novel randomized minimization algorithm doesn't require nested simulation. As main feature, possibly large efficiently select as close possible Doob martingale. result, one obtains upper bound for problem with low variance.