Prophet Compared to Gambler: An Inequality for Transforms of Processes
Krengel, Ulrich ; Sucheston, Louis
Ann. Probab., Tome 15 (1987) no. 4, p. 1593-1599 / Harvested from Project Euclid
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A prophet is a player with complete foresight; a gambler knows only the past and the present, but not the future. If each of them bets on differences of consecutive nonnegative random variables $X_i$ such that $E(X_i|X_{i - 1}) = EX_i$, the players multiplying their stakes by uniformly bounded variables, then the expected gain of the prophet is at most three times that of the gambler. The constant 3 is optimal.
Publié le : 1987-10-14
Classification:  Prophet inequality,  transforms of processes,  60G40 
@article{1176991996,
     author = {Krengel, Ulrich and Sucheston, Louis},
     title = {Prophet Compared to Gambler: An Inequality for Transforms of Processes},
     journal = {Ann. Probab.},
     volume = {15},
     number = {4},
     year = {1987},
     pages = { 1593-1599},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991996}
}

Krengel, Ulrich; Sucheston, Louis. Prophet Compared to Gambler: An Inequality for Transforms of Processes. Ann. Probab., Tome 15 (1987) no. 4, pp.  1593-1599. http://gdmltest.u-ga.fr/item/1176991996/