Reflected Backward Stochastic Differential Equations for a Finite State   Markov Chain Model and Applications to American Options
  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. 
Dimbinirina Ramarimbahoaka, Zhe Yang, Robert J. Elliott
math.PR