Relations between stochastic orderings and Generalized stochastic precedence

The concept of stochastic precedence between two real-valued random variables has often emerged in different applied frameworks. In this paper we analyze several aspects of a more general, and completely natural, concept of stochastic precedence that also had appeared in the literature. In particular, we study the relations with the notions of stochastic ordering. Such a study leads us to introducing some special classes of bivariate copulas. Motivations for our study can arise from different fields. In particular we consider the frame of Target-Based Approach in decisions under risk. This approach has been mainly developed under the assumption of stochastic independence between “Prospects” and “Targets”. Our analysis concerns the case of stochastic dependence.