The uniform local asymptotics of the bidimensional discounted aggregate claim process

Abstract

In this paper, we consider a bidimensional risk model with constant interest force, in which the claim size vector with the local subexponential marginal distributions and its inter-arrival time are subject to a local time-dependence structure.Moreover, we give some types of concrete joint distributions following the structure. Then we obtain the uniform local asymptotic expression of the discounted aggregate claim process and the total net loss process in the model.