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A Forward Algorithm for Solving Optimal Stopping Problems

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Albrecht Irle
Albrecht Irle*
Affiliation:
University of Kiel
*
∗ Postal address: Mathematisches Seminar, University of Kiel, Ludwig-Meyn-Strasse 4, D-24098 Kiel, Germany. Email address: irle@math.uni-kiel.de
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Abstract

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We consider the optimal stopping problem for g(Zn), where Zn, n = 1, 2, …, is a homogeneous Markov sequence. An algorithm, called forward improvement iteration, is presented by which an optimal stopping time can be computed. Using an iterative step, this algorithm computes a sequence B0 ⊇ B1 ⊇ B2 ⊇ · · · of subsets of the state space such that the first entrance time into the intersection F of these sets is an optimal stopping time. Various applications are given.

Keywords

Optimal stoppingalgorithm

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 102 - 113
Copyright
© Applied Probability Trust 2006 

References

Beibel, M. and Lerche, H. R. (1997). A new look at optimal stopping problems related to mathematical finance. Statistica Sinica 7, 93–108.Google Scholar
Chow, Y. S., Robbins, H. and Siegmund, D. (1971). Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston, MA.Google Scholar
Feller, W. (1957). An Introduction to Probability and Statistics, Vol. I, 2nd edn. John Wiley, New York.Google Scholar
Irle, A. (1980). On the best choice problem with random population size. Z. Operat. Res. 24, 177–190.Google Scholar
Shiryayev, A. N. (1978). Optimal Stopping Rules. Springer, New York.Google Scholar