  For three nonstandard renewal risk models, in which claim sizes are
identically distributed random variables with consistently varying tails, using
two key probability inequalities for wide dependent random variables, we study
precise large deviations of proportional net loss process and
excess-of-net-loss process under the consideration of income factor. Then we
apply the above results to obtain asymptotic estimate of mean of stop-net-loss
reinsurance treat and random-time ruin probability. In addition, we have
improved and generalized some known related results, none of which involve the
income factor.
