Abstract
This paper investigates some precise large deviations for the random sums of the differences between two sequences of independent and identically distributed random variables, where the minuend random variables have subexponential tails, and the subtrahend random variables have finite second moments. As applications to risk theory, the customer-arrival-based insurance risk model is considered, and some uniform asymptotics for the ruin probabilities of an insurance company are derived as the number of customers or the time tends to infinity. MSC: 60F10; 62E20; 62P05
Highlights
Introduction and main resultThroughout, let {Xk, k ≥ } be a sequence of independent and identically distributed (i.i.d.) nonnegative random variables (r.v.s) with a common distribution B, {Yk, k ≥ } be a sequence of i.i.d. nonnegative r.v.s
We are interested in the precise large deviations for the randomly index sums SN(t) under the assumption that the distribution B is heavy tailed
Precise large deviation probabilities for random sums have been extensively investigated by many researchers who have mainly concentrated on the sequence of nonnegative r.v.s, whose distributions belong to some subclasses of the classes S and D
Summary
Introduction and main resultThroughout, let {Xk, k ≥ } be a sequence of independent and identically distributed (i.i.d.) nonnegative random variables (r.v.s) with a common distribution B, {Yk, k ≥ } be a sequence of i.i.d. nonnegative r.v.s. We are interested in the precise large deviations for the randomly index sums (random sums) SN(t) under the assumption that the distribution B is heavy tailed. Precise large deviation probabilities for random sums have been extensively investigated by many researchers who have mainly concentrated on the sequence of nonnegative r.v.s, whose distributions belong to some subclasses of the classes S and D.
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