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A Forward Algorithm for Solving Optimal Stopping Problems

Part of: Markov processes Stochastic 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(Z n ), where Z n , 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 B 0 ⊇ B 1 ⊇ B 2 ⊇ · · · 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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 102 - 113
Copyright
© Applied Probability Trust 2006 

References

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