AN OPTIMAL STOPPING PROBLEM FOR RANDOM-WALKS WITH NONZERO DRIFT

In this paper we give a solution of an optimal stopping problem concer ning random walks (S-n)(n is an element of No) with non-zero drift, th ereby proving the necessity of the existence of ES(t) for Wald's equat ion ES(t)=ES(l) . E tau to hold, even if attention is restricted to no n-randomized stopping times tau. This answers a question of Robbins an d Samuel (1966).