Stochastic orderings for set-valued risk measures

This paper explores the portfolio aggregation problem within the framework of set-valued risk measures, with a specific emphasis on maximal correlation risk measures, as introduced in this work. We propose a novel stochastic ordering concept for random vectors and establish consistency properties for maximal correlation risk measures in this setting. Furthermore, we demonstrate convex-type consistency for a specific subclass of law-invariant convex set-valued risk measures, highlighting both their theoretical foundations and practical significance.