Tail Probabilities of Randomly Weighted Sums of Random Variables with Dominated Variation

Abstract

This paper investigates the asymptotic behavior of tail probabilities of randomly weighted sums of independent heavy-tailed random variables, where the weights form another sequence of nonnegative and arbitrarily dependent random variables. The results obtained are further applied to derive asymptotic estimates for the ruin probabilities in a discrete time risk model with dependent stochastic returns.