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Probability Maximizing Approach to Optimal Stopping of Random Fields

  • Roman Różański
  • Krzysztof Szajowski

Abstract

The paper deals with a problem of optimal stopping for non-negative random fields. As in Mandelbaum and Vanderbei (1981) we restrict ourselves to the class of predictable stopping points. A necessary and sufficient condition for existence an optimal strategy is given. The result is used to solve the probability maximizing version of the problem of optimal stopping for random fields indexed by a countable partially ordered set. It generalizes the probability maximizing approach to the problem of optimal stopping for stochastic processes formulated by Bojdecki (1978). We specialize our results to the problem of optimal stopping for several Markov chains. Examples concerning the problem of optimal allocation of different treatments and some problems of optimal selection are given.

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References

  1. T. Bojdecki (1978) On optimal stopping of a sequence of independent random variables — probability maximizing approach, Stochastic Proc. and their Appl., 6, pp. 153–163.CrossRefGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Roman Różański
    • 1
  • Krzysztof Szajowski
    • 1
  1. 1.Institute of MathematicsTechnical University of WrocławWrodawPoland

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