Stochastic orderings for set-valued risk measures

We analyze an extension of the maximal correlation risk measure in the set-valued scenario, based on Burgert and Rüschendorf (2006). We introduce stochastic ordering for random vectors using the upper expectation operator (Hamel and Heyde, 2021) and explore its consistency for set-valued risk measures. These measures, like law-invariant set-valued risk measures (e.g., set-valued distortion risk measure from Chen and Hu, 2019), offer flexibility in adhering to portfolio aggregator axioms and proper set-valued risk measure properties.