Precise large deviations of the net loss process in a non-standard two-dimensional risk model

Abstract This paper investigates the precise large deviations of the net loss process in a two-dimensional risk model with consistently varying tails and dependence structures, and gives some asymptotic formulas which hold uniformly for all x varying in t -intervals. The study is among the initial efforts to analyze potential risk via large deviation results for the net loss process of the two-dimensional risk model, and can provide a novel insight to assess the operation risk in a long run by fully considering the premium income factors of the insurance company.