Representations of set-valued risk measures defined on the $$l$$ l -tensor product of Banach lattices

Abstract

We obtain a representation for set-valued risk measures which are defined on the completed \(l\)-tensor product \(E\widetilde{\otimes }_l G\) of Banach lattices \(E\) and \(G\). This representation extends known representations for set-valued risk measures defined on Bochner spaces \(L^p(\mathbb {P}, \mathbb {R}^d)\) of \(p\)-integrable functions with values in \(\mathbb {R}^d\).