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 $\{S_n,n\ge 0\}$ with $S_0=0$ 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.

KEYWORDS AND PHRASES:

• Subexponential tails
• maxima of random sums
• time dependent
• renewal model

AMS 2000 Subject Classification:

• Primary: 60F10
• 60F05
• 60G05