Why is one choice different? |
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Authors: | David Assaf Ester Samuel-Cahn |
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Institution: | Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel |
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Abstract: | Let Xi be nonnegative independent random variables with finite expectations and . The value is what can be obtained by a “prophet”. A “mortal” on the other hand, may use k1 stopping rules t1,…,tk yielding a return Emaxi=1,…,kXti]. For nk the optimal return is where the supremum is over all stopping rules which stop by time n. The well known “prophet inequality” states that for all such Xi's and one choice and the constant “2” cannot be improved on for any n2. In contrast we show that for k=2 the best constant d satisfying for all such Xi's depends on n. On the way we obtain constants ck such that . |
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Keywords: | Optimal stopping rules Ratio prophet inequalities Multiple stopping options |
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