A note on convex stochastic dominance and diversification with applications

In this note, we present an overlooked result derived from Fishburn's Convex Stochastic Dominance (CSD) (Fishburn (1974a; 1974b). We demonstrate that CSD is a sufficient condition for establishing second-order stochastic dominance in the context of linear combinations of random variables. While this result may appear straightforward, to the best of our knowledge, it has not been explicitly presented as we have done in this work. Furthermore, the implications of this finding are extensive, as it can be applied to various areas of research, as we illustrate in this study.