In this paper a study on Second and Third degree Stochastic Dominances for the family of concave and convex utility functions is proposed. This is the LDEU model case, which is more general than the classical expected utility model. We prove that Second and Third Stochastic Dominances can be applied respecting this new axiomatic. In addition, in the context of LDEU model, we can explain in a rational way, the violation of the Second Stochastic Inverse Dominance SSID (Alais paradox) as a consequence of the change in a local aversion to risk.