Stochastic comparisons of aggregate claim amounts under Archimedean copula

This paper studies some usual stochastic ordering properties of aggregate claim amounts under the Archimedean copula. Some results on the usual stochastic order of aggregate claim amounts in the independent case are shown to still hold when the random variables are dependent under the Archimedean copula. Thus, these results generalize some known results in the literature. An example is also provided to illustrate the established results.