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Optimal Stopping in a Dice Game

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Markus Roters
Markus Roters*
Affiliation:
Universität Trier
*
∗Postal address: FB IV Mathematik/Statistik, Universität Trier, D-54286 Trier, Germany
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Abstract

In this paper we consider an explicit solution of an optimal stopping problem arising in connection with a dice game. An optimal stopping rule and the maximum expected reward in this problem can easily be computed by means of the distributions involved and the specific rules of the game

Keywords

Central limit theoremgamblinggame theoryMarkov decision theoryoptimal stoppingrenewal theory

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60J05: Discrete-time Markov processes on general state spaces
Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 229 - 235
Copyright
Copyright © Applied Probability Trust 1998 

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References

Chow, Y. S., Robbins, H., and Siegmund, D. (1991). The Theory of Optimal Stopping. Dover, New York.Google Scholar
Dubins, L. E., and Teicher, H. (1967). Optimal stopping when the future is discounted. Ann. Math. Statist. 38, 601–605.Google Scholar
Ferguson, T. S. (1976). Stopping a sum during a success run. Ann. Statist. 4, 252–264.Google Scholar
Gut, A. (1988). Stopped Random Walks. Limit Theorems and Applications. Springer, New York.Google Scholar
Haggstrom, G. W. (1967). Optimal sequential procedures when more than one stop is required. Ann. Math. Statist. 38, 1618–1626.CrossRefGoogle Scholar
Karlin, S., and Taylor, H. M. (1981). A Second Course in Stochastic Processes. Academic Press, Boston.Google Scholar
Schäl, M. (1990). Markoffsche Entscheidungsprozesse. Teubner, Stuttgart.CrossRefGoogle Scholar