BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH NO DRIVING MARTINGALE AND PSEUDO-PDEs

We discuss a 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 Markovian BSDEs. Moreover they can be associated to a deterministic problem, called Pseudo-PDE. That problem constitutes the natural generalization of the parabolic semilinear PDE which naturally appears when the underlying filtration is Brownian. We consider two aspects of well-posedness for the Pseudo-PDEs: classical and martingale solutions.