Quadratic transformations of multivariate semi-copulas

Abstract

In this study, we introduce a construction of semi-copulas via a composition of multivariate semi-copulas with a quadratic polynomial. Obviously, such compositions will not always result in a semi-copula. Our main focus is to provide a characterization of such polynomials in terms of their coefficients. We found that the set of those coefficients forms a convex set with a linear boundary. We also found that several such transformations that are not a convex combination of semi-copulas.