  In this paper, we address the stochastic representation problem in discrete
time under (non-linear) g-expectation. We establish existence and uniqueness of
the solution, as well as a characterization of the solution. As an application,
we investigate a new approach to the optimal stopping problem under
g-expectation and the related pricing of American options under Knightian
uncertainty. Our results are also applied to a (non-linear) Skorokhod-type
obstacle problem.
