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For three nonstandard renewal risk models, in which claim sizes areidentically distributed random variables with consistently varying tails, usingtwo key probability inequalities for wide dependent random variables, we studyprecise large deviations of proportional net loss process andexcess-of-net-loss process under the consideration of income factor. Then weapply the above results to obtain asymptotic estimate of mean of stop-net-lossreinsurance treat and random-time ruin probability. In addition, we haveimproved and generalized some known related results, none of which involve theincome factor.

Precise large deviations of some net loss processes in three nonstandard renewal risk models