Shen, L.Elliott, R.2013-06-252013-06-252012Methodology and Computing in Applied Probability, 2012; 14(4):955-9711387-58411573-7713http://hdl.handle.net/2440/78472We define Backward Stochastic Difference Equations related to a discrete finite time single jump process. We prove the existence and uniqueness of solutions under some assumptions. A comparison theorem for these solutions is also given. Applications to the theory of nonlinear expectations are then investigated. In this paper the single jump process takes values in a general measurable space where as previous work has considered the situation where the noise is a finite state Markov chain, so the state space is finite.en© Springer Science+Business Media, LLC 2011Single jump processBSDEComparison theoremNon-linear expectationDynamic risk measure60H1060G4265C30Journal article002012286510.1007/s11009-011-9217-z0003102288000042-s2.0-8486790197422652