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In this paper, we introduce a new kind of reflected backward stochasticdifferential equations (RBSDEs) driven by a martingale, in a Markov chainmodel, but not driven by Brownian motion, and give existence and uniquenessresults for the new equations. Then we discuss American options in a finitestate 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 aconstrained super-hedging strategy for an American option, which is unique inour framework as the solution to an RBSDE.

Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model and Applications to American Options