We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations...

By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions in their own right, not as approximations to the...

Cohen and Elliott (2010) introduced the backward stochastic difference equations (BSDEs) on spaces related to discrete time, finite state processes. Motivated by obtaining the explicit solution of a linear BSDE under their framework, we develop a new type of Girsanov transformation in this paper.