Estimations for aggregate amount of claims in a risk model with arbitrary dependence between claim sizes and inter-arrival times

Abstract

This paper considers a compound risk model, in which the individual claim sizes and their inter-arrival times can be arbitrarily dependent. We mainly investigate the claim sizes are extended negatively dependent. When the claim sizes have consistently-varying-tailed distributions, we obtain precise large deviations of the aggregate amount of claims in the above dependent compound risk model.

Keywords

• precise large deviations
• compound sums
• extended negative dependence
• consistently varying distribution