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

Dimbinirina Ramarimbahoaka, Zhe Yang, Robert J. Elliott

Published 2014-04-08, updated 2014-11-27Version 4

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.