A note on the max-sum equivalence of randomly weighted sums of heavy-tailed random variables

Abstract

This paper investigates the asymptotic behavior for the tail probability of the randomly weighted sums ∑_k=1ⁿθ_kX_k and their maximum, where the random variables X_k and the random weights θ_k follow a certain dependence structure proposed by Asimit and Badescu [1] and Li et al. [2]. The obtained results can be used to obtain asymptotic formulas for ruin probability in the insurance risk models with discounted factors.