On Markovian solutions to Markov Chain BSDEs
  We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows us to connect these equations to coupled systems of ODEs, and hence to give fast numerical methods for the evaluation of Markov-Chain BSDEs. 
Samuel N. Cohen and Lukasz Szpruch
math.PR math.CA q-fin.CP