Asymptotics of randomly weighted sums without moment conditions of random weights

TL;DR

This paper studies the asymptotic behavior of randomly weighted sums without moment conditions on weights, providing new theoretical insights and applications to risk models with heavy-tailed increments.

Contribution

It introduces novel asymptotic results for weighted sums without moment assumptions and extends Breiman's theorem for regularly varying tails.

Findings

Derived asymptotic estimates for ruin probabilities in risk models.

Established results under new conditions without moment assumptions.

Extended Breiman's theorem for heavy-tailed increments.

Abstract

In the paper, we investigate the asymptotic behaviors of the randomly weighted sums with upper tail asymptotically independent increments under new conditions without requiring moment assumptions on random weights.An application of the obtained results is established to asymptotically estimate for finite-time ruin probability in a discrete-time risk model. For the case of increments with regularly varying tails, we obtain more explicit results via an extension of Breiman's theorem.