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Asymptotics for a Type of Randomly Weighted Sums and Its Application

This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,igeq1} is a sequence of independent, identically distributed and real-valued random variables and the weights {theta_i,igeq1} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the Fbelongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability.