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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Utility functions which ensure the adequacy of stationary strategies


Author: Michael G. Monticino
Journal: Trans. Amer. Math. Soc. 325 (1991), 187-204
MSC: Primary 60G40; Secondary 62L15, 90A10, 90D35
DOI: https://doi.org/10.1090/S0002-9947-1991-0998355-1
MathSciNet review: 998355
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Abstract: Within a Dubins and Savage gambling framework, a stationary strategy is a strategy which selects a gamble at each time based solely on the gambler's present fortune. We determine conditions upon the gambler's utility function under which stationary strategies allow the gambler to maximize his return. The class of utility functions which satisfies these conditions, termed nearly leavable shift invariant functions, is large and contains many of the common gambling utility functions. Moreover, this class is closed under uniform limits. These results are obtained with the setting of an analytic gambling house.


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DOI: https://doi.org/10.1090/S0002-9947-1991-0998355-1
Keywords: Gambling, optimal return, stationary strategies, utility function
Article copyright: © Copyright 1991 American Mathematical Society