Randomly weighted sums of conditionally dependent and dominated varying-tailed increments with application to ruin theory

In this paper, we obtain the weakly asymptotic formulas of the tail probabilities of randomly weighted sums and their maximum of dominated varying-tailed random variables under a general conditional dependence structure, where the corresponding random weights can take values in the whole real space. The obtained results extend and improve some existing ones. An application of the weakly asymptotic formulas is proposed to estimate the ruin probability in a discrete-time risk model.