We define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with the same marginals. Moreover, some properties and relations of stochastic orders are discussed.
"Two Sufficient Conditions for Convex Ordering on Risk Aggregation." Abstr. Appl. Anal. 2018 1 - 5, 2018. https://doi.org/10.1155/2018/2937895