Precise large deviations for non-centralized sums of partial sums and random sums of heavy-tailed END random variables (Q6580267)

The authors consider an insurance company having \(d\) types of insurance contracts and regard \(X_{ij}\) as the \(j\)-th claim size in the \(i\)-th insurance contract, then the aggregate amount of claims up to time \(t\) is a random sum of the form \(S_d(t)=\sum_{i=1}^{N(t)}S_{N_i(t)}=\sum_{i=1}^{N(t)}\sum_{j=1}^{N_i(t)}X_{ij}, \;i=1,\ldots, d.\)\N\NThe authors obtain some asymptotic upper and lower bounds of precise large deviations for non-centralized sums of partial sums and random sums, where the summands are extended negatively dependent random variables with dominatedly-varying-tailed distributions supported on \((-\infty,+\infty).\)