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- W2083405417 abstract "Let Xi be nonnegative independent random variables with finite expectations and Xn*=max{X1,…,Xn}. The value EXn* is what can be obtained by a “prophet”. A “mortal” on the other hand, may use k⩾1 stopping rules t1,…,tk yielding a return E[maxi=1,…,kXti]. For n⩾k the optimal return is Vkn(X1,…,Xn)=supE[maxi=1,…,kXti] 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 EXn*<2V1n(X1,…,Xn) and the constant “2” cannot be improved on for any n⩾2. In contrast we show that for k=2 the best constant d satisfying EXn*<dV2n(X1,…,Xn) for all such Xi's depends on n. On the way we obtain constants ck such that EXk+1*<ckVkk+1(X1,…,Xk+1)." @default.
- W2083405417 created "2016-06-24" @default.
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- W2083405417 date "2005-03-01" @default.
- W2083405417 modified "2023-09-25" @default.
- W2083405417 title "Why is one choice different?" @default.
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- W2083405417 doi "https://doi.org/10.1016/j.jspi.2004.01.023" @default.
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