On Randomized Tactics and Optimal Stopping in the Plane

Abstract

Given a two-parameter filtration $(\mathscr{F}_z)$ satisfying the conditional independence assumption (F4), we prove the existence of an optimal stopping point for adapted processes $(X_z)$ indexed by $\mathbb{N}^2$ or $\mathbb{R}^2_+$ which are of class $(D)$, and have regularity properties which generalize the usual one-parameter ones, and are expressed in terms of sequences of 1- and 2-stopping points.