Backward stochastic differential equations with jumps and related non-linear expectations

In this paper, we are interested in real-valued backward stochastic differential equations with jumps together with their applications to non-linear expectations. The notion of non-linear expectations has been studied only when the underlying filtration is given by a Brownian motion and in this work the filtration will be generated by both a Brownian motion and a Poisson random measure. We study at first backward stochastic differential equations driven by a Brownian motion and a Poisson random measure and then introduce the notions of f$f$-expectations and of non-linear expectations in this set-up.