@booklet {samuel-cahn-wiocd2003,
	title = {Why Is One Choice Different?},
	howpublished = {Discussion Papers},
	year = {2003},
	month = {9},
	publisher = {Journal of Statistical Planning and Inference 130 (2005), 127-132},
	abstract = {Let Xi be nonnegative independent random variables with finite expectations and Xn* = max X1,..., Xn. The value Xn* is what can be obtained by a "prophet". A "mortal" onthe other hand, may use k {\textquoteright}{\textyen} 1 stopping rules t1,...,tk yielding a return E[max i = 1,...,k X ti]. For n {\textquoteright}{\textyen} k the optimal return is Vkn (X1,...,Xn) = sup E[max i = 1,...,k X ti] where the supremum is over all stopping rules which stop by time n. The well known "prophet inequality" states that for all such Xi{\textquoteright}s and one choice EXn* < 2 V1n (X1,...,Xn) and the constant "2" cannot be improved on for any n {\textquoteright}{\textyen} 2. In contrast we show that for k=2 the best constant d satisfying EXn* < d V2n (X1,...,Xn) for all such Xi{\textquoteright}s depends on n. On the way we obtain constants ck such that EXk+1* < ck Vkk+1 (X1,...,Xk+1).},
	url = {/files/dp335.pdf},
	author = {Samuel-Cahn, David Assaf and Ester}
}
