The Annals of Probability
- Ann. Probab.
- Volume 15, Number 4 (1987), 1593-1599.
Prophet Compared to Gambler: An Inequality for Transforms of Processes
Ulrich Krengel and Louis Sucheston
Abstract
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.
Article information
Source
Ann. Probab., Volume 15, Number 4 (1987), 1593-1599.
Dates
First available in Project Euclid: 19 April 2007
Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991996
Digital Object Identifier
doi:10.1214/aop/1176991996
Mathematical Reviews number (MathSciNet)
MR905351
Zentralblatt MATH identifier
0637.60057
JSTOR
links.jstor.org
Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Keywords
Prophet inequality transforms of processes
Citation
Krengel, Ulrich; Sucheston, Louis. Prophet Compared to Gambler: An Inequality for Transforms of Processes. Ann. Probab. 15 (1987), no. 4, 1593--1599. doi:10.1214/aop/1176991996. https://projecteuclid.org/euclid.aop/1176991996
