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A Stopping Problem

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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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© 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

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