The Gambler and the Stopper

A gambler (or stochastic controller) selects the distribution for the stochastic process x, X1, X2,... from those available in a given gambling house. An optimal stopper selects a stop rule t and pays the gambler the expected value of$u(X_{t})$, where u is a bounded, real-valued function. Under cert...

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Bibliographic Details
Published in:Lecture notes-monograph series 1996-01, Vol.30, p.191-208
Main Authors: Maitra, Ashok P., Sudderth, William D.
Format: Article
Language:English
Subjects:
Descriptive set theory
Dynamic programming
Expected values
Gambling
Game theory
Mathematical functions
Mathematical inequalities
Mathematical set theory
Mathematics
Stochastic games
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Summary:A gambler (or stochastic controller) selects the distribution for the stochastic process x, X1, X2,... from those available in a given gambling house. An optimal stopper selects a stop rule t and pays the gambler the expected value of$u(X_{t})$, where u is a bounded, real-valued function. Under certain measurability assumptions, this game has a value and there is a transfinite algorithm for calculating it.
ISSN:0749-2170