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- W2029895767 abstract "An urn contains N balls, labelled 1,…,N. Optimal stopping rules are considered for payoff functions f(k, m) where f(k, m) is the reward when stopping after k draws, and the largest number seen by then is m. f(k, m) is assumed nondecreasing i m for each k. We show: (i) For any horizon n ⩽ N, under optimal stopping, sampling without replacement yields a larger expected value than sampling with replacement. (ii) A sufficient condition, both when sampling with or without replacement, for the optimal stopping rule to be of the form t =inf{k:Mk ⩾qk} for some constants qk, where Mk is the maximal label Δ(k, m) = f(k, m + 1) − f(k, m) be nonincreasing in k for each m. Better sufficient conditions are given, and several e such as reward minus cost of sampling, or discounted rewards, are considered. Some limiting results, as N →∞, and prophet inequality considerations are included for the example where the payoff is reward minus cost of sampling." @default.
- W2029895767 created "2016-06-24" @default.
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- W2029895767 date "1993-04-01" @default.
- W2029895767 modified "2023-09-27" @default.
- W2029895767 title "Optimal stopping in urn models with payoff depending on maximal observed element" @default.
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- W2029895767 doi "https://doi.org/10.1016/0167-7152(93)90070-y" @default.
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