Backward Stochastic Differential Equations on Markov Chains with Non-Lipschitz Coefficients

In this paper, we study the well-posedness of stochastic systems whose state processes are governed by a class of backward stochastic differential equations related to finite state, continuous time Markov chains. We establish the existence, uniqueness of solutions for these equations under non-Lipschitz conditions. The results play a crucial role in optimal stochastic control in random environment and also can expand the applications.