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

  • Shijie Wang (a1) and Wensheng Wang (a2)
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.

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Copyright
Corresponding author
Postal address: Department of Statistics, East China Normal University, Shanghai 200062, P. R. China.
∗∗ Email address: ahuwsj@126.com
∗∗∗ Email address: wswang@stat.ecnu.edu.cn
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