Uniform asymptotic behavior of tail probability of maxima in a time-dependent renewal risk model

Abstract

In this article, we investigate the uniform asymptotic behavior for the tail probability of maxima of a random walk with and negative drift. We establish the tail probability in the frame of a time-dependent renewal risk model. In this model, we assume that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs. Furthermore, we suppose the tail probability distribution belongs to the strongly subexponential class.