Precise large deviations of some risk objectives related to the net loss process in two nonstandard risk models

Abstract

For two nonstandard renewal risk models, we investigate the precise large deviations of the finite-time ruin probability and a random sum of the net-loss process, and the asymptotics of the random-time ruin probability. Notably, in one of these models, claim sizes series and claim interval time series are allowed to be arbitrarily dependent. Subsequently, we apply these results to obtain precise large deviations of proportional-net-loss process and excess-of-net-loss process, as well as asymptotic estimates of the mean of stop-net-loss reinsurance treaty. These results all involve the income items of the risk model, which are relatively rare in the existing references.