The premium of the sum of two risks X and Y with positive dependence PQD and NQD negative dependence and its impact is studied in this paper using copulas as the general structure that governs such dependence. We propose a demonstration of Hoeffding's lemma and is used to calculate the variance of . X Y+ Various premium principles (variance, standard deviation, variance as amended) and most commonly used measures of dependence ( of Kendall, dependence on the tail) are propoused and used. Several numerical examples risks of dependence with some Archi­medean copulas are presented.