Random walks with long-tailed increments have many important applications in insurance, finance, queueing networks, storage processes, and the study of extreme events in nature and elsewhere. See, for example, Embrechts et al. (1997), Asmussen (1998, 1999) and Greiner et al. (1999) for some background. In this paper we study the distribution of the maximum of such a random walk over a random ti...
