Abstract
We consider a dependent compound renewal risk model, where the interarrival times of accidents and the claim numbers follow a dependence structure characterized by a conditional tail probability and the claim sizes have a pairwise negatively quadrant dependence structure or a related dependence structure with the upper tail asymptotical dependence structure. When the distributions of the claim sizes belong to the dominated variation distribution class, we give the asymptotic lower and upper bounds for the precise large deviations of the aggregate claims.
Highlights
Consider the compound renewal risk model where the claim sizes {Xij, j ≥ 1} caused by the ith (i ≥ 1) accident form a sequence of nonnegative random variables (r.v.s) with finite mean
In this paper, when investigating the asymptotic upper bound of the precise large deviations of the aggregate claims, we consider the claim sizes that have a pairwise negatively quadrant dependence structure
Liu et al [21] obtained the asymptotic lower bound of the precise large deviations of the aggregate claims when F ∈ L ∩ D and {Xij, i ≥ 1, j ≥ 1} satisfy the dependence structure (1.2)
Summary
Consider the compound renewal risk model where the claim sizes {Xij, j ≥ 1} caused by the ith (i ≥ 1) accident form a sequence of nonnegative random variables (r.v.s) with finite mean. The interarrival times of the accidents {θi, i ≥ 1} are positive independent identically distributed (i.i.d.) r.v.s with finite mean λ–1. Let {Yi, i ≥ 1} be the claim numbers caused by the successive accidents, which are a sequence of i.i.d. positive integer-valued r.v.s with finite mean ν. We assume that the r.v.s {Yi, i ≥ 1} are bounded, that is, there exists a finite integer number h > 0 such that Yi ≤ h, i ≥ 1. The aggregate claims accumulated up to time t ≥ 0 are expressed as. We investigate the precise large deviations for the random sums S(t)
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