Martingale matrix classes and polytopes

Martingale theory plays a central role in modern probability, stochastic analysis and related areas. Martingales with finite time and probability space may be viewed as matrices satisfying certain conditions. We study such martingale matrix classes and related polytopes. In particular, we determine the extreme points of a polytope PM of probability vectors for which a given matrix M is a martingale. This polytope is of interest in mathematical finance.