Coskewness under dependence uncertainty.

We study the impact of dependence uncertainty on E (X 1 X 2 ⋯ X d) , X i ∼ F i . Under some conditions on the F i , explicit sharp bounds are obtained. A numerical method is provided to approximate them for arbitrary F i. We introduce a notion of "standardized rank coskewness", which is invariant under strictly increasing transformations and takes values in [ − 1 , 1 ]. • Derive sharp bounds for E (X 1 X 2 ⋯ X d) , X i ∼ F i , under dependence uncertainty and some assumptions on F i. • Design an algorithm to approximate the sharp bounds for general F i. • Introduce the new concept of "standardized rank coskewness". [ABSTRACT FROM AUTHOR]