  In this paper, we first establish the reflected backward stochastic
difference equations with finite state (FS-RBSDEs for short). Then we explore
the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one
step" method. The connections between FS-RBSDEs and optimal stopping time
problems are investigated and we also show that the optimal stopping problems
with multiple priors under Knightian uncertainty is a special case of our
FS-RBSDEs. As a byproduct we develop the general theory of g-martingales in
discrete time with finite state including Doob-Mayer Decomposition Theorem and
Optional Sampling Theorem. Finally, we consider the pricing models of American
Option in both complete and incomplete markets.

Probability;Optimization and Control;Computational Finance