Asymptotics for the partial sum and its maximum of dependent random variables*

Abstract

Let X1,…,Xn be pairwise asymptotically independent or pairwise upper extended negatively dependent real-valued random variables. Under the condition that the distribution of the maximum of X1,…,Xn belongs to some subclass of heavy-tailed distributions, we investigate the asymptotic behavior of the partial sum and its maximum generated by dependent X1,…,Xn. As an application, we consider a discrete-time risk model with insurance and financial risks and derive the asymptotics for the finite-time ruin probability.