The First Passage Time Problem Over a Moving Boundary for Asymptotically Stable Levy Processes

摘要

We study the asymptotic tail behaviour of the first passage time over a moving boundary for asymptotically -stable L,vy processes with . Our main result states that if the left tail of the L,vy measure is regularly varying with index , and the moving boundary is equal to for some , then the probability that the process stays below the moving boundary has the same asymptotic polynomial order as in the case of a constant boundary. The same is true for the increasing boundary with under the assumption of a regularly varying right tail with index -alpha.