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An urn contains N objects, labelled with the integers 1, , N. One object is removed at a time, without replacement. If after n draws the largest number which has been observed is mₙ, and the process is terminated, we receive a payoff f (n, mₙ). For payoff functions f in a certain class, the optimal time to stop is with draw f = \n 0: mₙ - n jₙ\ where the jₙ are computable from a simple algorithm, which permits also exact computation of the value Vf = E\f (f, m₅) \. We also study the behavior of Vf when N is large in special cases.
Chen et al. (Sun,) studied this question.