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this paper we study the distribution of the maximumof such a random walk over a random time interval.Let F be the distribution function of the increments of a random walk{Sn}n#0 withS 0 = 0. Suppose that this distribution has a finite negative mean and that F is longtailedin the positive direction (see below for this and other definitions). Of interest is theasymptotic distribution of the maximum of{Sn}over the interval [0,#] defined by somestopping time #. Some results...

The maximum on a random time interval of a random walk with long-tailed increments and negative drift