Asymptotic Tail Probability of Randomly Weighted Sum of Dependent Heavy-Tailed Random Variables

Abstract

This paper investigates the asymptotic behavior of tail probability of a randomly weighted sum of real-valued heavy-tailed dependent random variables; the weights form another sequence random variable. Under some other mild conditions, the asymptotic relations obtained are further applied to derive asymptotic estimate for ruin probabilities in a discrete time risk model.

On the tail behavior for randomly weighted sums of dependent random variables with its applications to risk measures

“…Yi et al (2011) [43] followed their work by extending the distributions of F 1 and F 2 to be dominatedly-varying-tailed, however, they found it hard to obtain the precise asymptotic formula for H 1 ⊕ H 2 like (1.2) and derived the asymptotic upper and lower bounds for it. For some other dependence structures making (1.2) valid, we refer the reader to Chen et al (2010) [9], Gao and Jin (2015) [19], Wang (2011) [37], and Wang et al (2014) [40] for strongly quasiasymptotic independence; Wang et al (2016) [38], Yang et al (2012) [41] for time-dependence structure; Cheng and Cheng (2018) [11], Geng et al (2019) [21], and Gao and Liu (2020) [20] for conditionally linearly wide dependence.…”