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Gambling Problems with a Limit Inferior Payoff
William D. Sudderth
Mathematics of Operations Research
Vol. 8, No. 2 (May, 1983), pp. 287-297
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3689594
Page Count: 11
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In the gambling theory of Dubins and Savage, the payoff from a sequence of states is the limit superior of their utilities. Here the limit inferior is used instead. For example, if the utility function is the indicator of a set G, then the Dubins and Savage payoff is 1 when infinitely many states are in G, while the payoff here is 1 when all but finitely many states are in G. There are some resulting changes in the theory, but it remains true that optimal stationary plans exist for finite problems.
Mathematics of Operations Research © 1983 INFORMS