Does positive dependence between individual risks increase stop-loss premiums?

Actuaries intuitively feel that positive correlations between individual ri sks reveal a more dangerous situation compared to independence. The purpose of this short note is to formalize this natural idea. Specifically, it is shown that the sum of risks exhibiting a weak form of positive dependence k nown as positive cumulative dependence is larger in convex order than the c orresponding sum under the theoretical independence assumption. (C) 2001 El sevier Science B.V. All rights reserved.