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

By M Denuit, Jan Dhaene and C Ribas

Abstract

Actuaries intuitively feel that positive correlations between individual risks 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 dependence known as positive cumulative dependence is larger in convex order than the corresponding sum under the theoretical independence assumption.Dependence; Risk;

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