Solutions of Backward Stochastic Differential Equations on Markov Chains
  We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We do not require the generating functions to be monotonic, instead using only an appropriate Lipschitz continuity condition. 
Samuel N. Cohen and Robert J. Elliott