The policy iteration method for the optimal stopping of a Markov chain with an application

K.M. Hee, van

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    Abstract

    In this paper we study the problem of the optimal stopping of a Markov chain with a countable state space. In each state i the controller receives a reward r(i) if he stops the process or he must pay the cost c(i) otherwise. We show that, under the condition that there exists an optimal stopping rule, the policy iteration method, introduced by Howard, produces a sequence of stopping rules for which the expected return converges to the value function. For random walks on the integers with a special reward and cost structure, we show that the policy iteration method gives the solution of a discrete two point boundary value problem with a free boundary. We give a simple algorithm for the computation of the optimal stopping rule.
    Original languageEnglish
    Title of host publicationOptimization techiques : modeling and optimization in the service of man part 2 (Proceedings 7th IFIP Conference, Nice, France, September 8-12, 1975), Part 2
    EditorsJ. Cea
    Place of PublicationBerlin
    PublisherSpringer
    Pages22-36
    Number of pages15
    ISBN (Electronic)978-3-540-38150-1
    ISBN (Print)3-540-07623-9
    DOIs
    Publication statusPublished - 1976

    Publication series

    NameLecture Notes in Computer Science
    Volume41
    ISSN (Print)0302-9743

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