Backward Stochastic Differential Equations with Continuous Coefficients   in a Markov Chain Model and with Applications to European Options
  In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for this kind of equation and derive the corresponding comparison result. This is applied to pricing of European options in a market with Markov chain noise. 
Dimbinirina Ramarimbahoaka, Zhe Yang, Robert J. Elliott
math.PR