Wang, Shijie; Wang, Wensheng Precise large deviations for sums of random variables with consistently varying tails in multi-risk models. (English) Zbl 1134.60322 J. Appl. Probab. 44, No. 4, 889-900 (2007). Summary: Assume that there are \(k\) types of insurance contracts in an insurance company. The \(i\)th related claims are denoted by \(\{X_{ij}\), \(j\geq 1\}\), \(i=1,\dots,k\). In this paper we investigate large deviations for both partial sums \(S(k;n_1,\dots,n_k)= \sum_{i=1}^k \sum_{j=1}^{n_i}X_{ij}\) and random sums \(S(k;t)= \sum_{i=1}^k \sum_{j=1}^{N_i(t)} X_{ij}\), where \(N_i(t)\), \(i=1,\dots,k\), are counting processes for the claim number. The obtained results extend some related classical results. Cited in 2 ReviewsCited in 31 Documents MSC: 60F10 Large deviations 60F05 Central limit and other weak theorems 60G50 Sums of independent random variables; random walks 91B30 Risk theory, insurance (MSC2010) Keywords:large deviation; loss process; consistently varying tail; sums of random variables PDFBibTeX XMLCite \textit{S. Wang} and \textit{W. Wang}, J. Appl. Probab. 44, No. 4, 889--900 (2007; Zbl 1134.60322) Full Text: DOI Euclid