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

Abstract

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