A Kesten-type bound for sums of randomly weighted subexponential random variables

Abstract

Sums of randomly weighted subexponential random variables have become an important research topic, but most works on the topic consider randomly weighted sums of finitely many terms. To extend the study to the case of infinitely many terms, we establish a Kesten-type upper bound for the tail probabilities of sums of randomly weighted subexponential random variables. As an application, we derive a precise asymptotic formula for the tail probability of the aggregate present value of subexponential claims, where the present value factor is determined according to the zero-coupon bond price.