Precise large deviations for sums of random variables with consistently varying tails in multi-risk models

摘要

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,center dot center dot center dot, k. In this paper we investigate large deviations for both partial sums S(k; n(1),center dot center dot center dot, n(k)) = Sigma(k)(i=1) Sigma(ni)(j=1) Xij and random sums S(k; t) = Sigma(k)(i=1) Sigma(Ni(t))(j=1) where N-i(t), i = 1,center dot center dot center dot, k, are counting processes for the claim number. The obtained results extend some related classical results.