Abstract : We investigate existence and uniqueness for a new class of Backward Stochastic Differential Equations (BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process X those BSDEs are denominated forward BSDEs and can be associated to a deter-ministic problem, called Pseudo-PDE which constitute the natural generalization of a parabolic semilinear PDE which naturally appears when the underlying filtration is Brownian. We consider two types of solutions for the Pseudo-PDEs: classical and of martingale type.
