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In this paper, we obtain some results on precise large deviations fornon-random and random sums of widely dependent random variables with commondominatedly varying tail distribution or consistently varying tail distributionon $(-\infty,\infty)$. Then we apply the results to reinsurance and insuranceand give some asymptotic estimates on proportional reinsurance, random-timeruin probability and the finite-time ruin probability.

Precise large deviations of sums of widely dependent random variables and its applications