Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-Risk Models

Abstract

Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {X ij , j ≥ 1}, i = 1,…,k. In this paper we investigate large deviations for both partial sums S(k; n 1,…,n k ) = ∑ i=1 k ∑ j=1 n i X ij and random sums S(k; t) = ∑ i=1 k ∑ j=1 N i (t) X ij , where N i (t), i = 1,…,k, are counting processes for the claim number. The obtained results extend some related classical results.