  In this paper, we introduce a new kind of reflected backward stochastic
differential equations (RBSDEs) driven by a martingale, in a Markov chain
model, but not driven by Brownian motion, and give existence and uniqueness
results for the new equations. Then we discuss American options in a finite
state Markov chain model, in the presence of a stochastic discount function
(SDF) and using the theory of the new RBSDEs. We show that there exists a
constrained super-hedging strategy for an American option, which is unique in
our framework as the solution to an RBSDE.
