Precise large deviations for the aggregate claims in a dependent compound renewal risk model

Abstract

Abstract We consider a dependent compound renewal risk model, where the interarrival times of accidents and the claim numbers follow a dependence structure characterized by a conditional tail probability and the claim sizes have a pairwise negatively quadrant dependence structure or a related dependence structure with the upper tail asymptotical dependence structure. When the distributions of the claim sizes belong to the dominated variation distribution class, we give the asymptotic lower and upper bounds for the precise large deviations of the aggregate claims.

Keywords

• Compound renewal risk model
• Precise large deviations
• The dominated variation class
• Upper tail asymptotically independence
• Pairwise negatively quadrant dependence