Martingale Inequalities under G-Expectation and Their Applications

In this paper, we study the martingale inequalities under G -expectation and their applications. To this end, we introduce a new kind of random time, called G -stopping time, and then investigate the properties of a G -martingale (supermartingale) such as the optional sampling theorem and upcrossing inequalities. With the help of these properties, we can show the martingale convergence property under G -expectation.