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A Stopping Problem

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Mathematical Modelling in Economics

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Abstract

A stopping time N = f(So,…,Sn) is used to monitor the fluctuation of a random walk (Sn). The random variable N is the stage at which Sn exceeds a predetermined bound for the first time. An extrapolation method is suggested giving monotone upper and lower bounds to the distribution function of N at each stage of iteration. The extrapolation method is based on the Perron-Frobenius theory of positive matrices and its generalization. The stopping problem is applied to some well-known models arising in quality control, risk theory, and queueing theory.

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Author information

Authors and Affiliations

  1. Institut für Wirtschaftstheorie und Operations Research, Universität Karlsruhe, Germany

    Karl-Heinz Waldmann

Authors
  1. Karl-Heinz Waldmann
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Editors and Affiliations

  1. Department of Economics, University of British Columbia, #997-1873 East Mall, V6T 1W5, Vancouver, B.C., Canada

    W. Erwin Diewert

  2. University of Hong Kong, K.K. Leung Building, Hong Kong

    Klaus Spremann

  3. Department of Economics, University of Ulm, Helmholtzstraße 18, D-89069, Ulm/Donau, Germany

    Frank Stehling

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© 1993 Springer-Verlag Berlin · Heidelberg

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Waldmann, KH. (1993). A Stopping Problem. In: Diewert, W.E., Spremann, K., Stehling, F. (eds) Mathematical Modelling in Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78508-5_46

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  • DOI: https://doi.org/10.1007/978-3-642-78508-5_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-78510-8

  • Online ISBN: 978-3-642-78508-5

  • eBook Packages: Springer Book Archive

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