Current open questions in complete mixability

Abstract: Complete and joint mixability has raised considerable interest in recent few years, in both the theory of distributions with given margins, and applications in discrete optimization and quantitative risk manage-ment. We list various open questions in the theory of complete and joint mixability, which are mathematically concrete, and yet accessible to a broad range of researchers without specific background knowledge. In addition to the discussions on open questions, some results contained in this paper ar