Some Research On Backward Stochastic Differential Equation Driven By G-expectation

This paper makes some research on backward stochastic differential equation driv-en by G-expectation (short G-BSDE). We obtain three main results. First, we expand the equivalent characterization for homogeneity and convexity of nonlinear expecta-tion driven by G-BSDE in the existing documents. Second, we get a necessary and sufficient condition of Jensen’s inequality under nonlinear expectation driven by G-BSDE. Third, we prove the 2-dimensional Jensen’s inequality, Holder’s inequality and Minkowski’s inequality under nonlinear expectation driven by G-BSDE.