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Foundations of Non-stationary Dynamic Programming with Discrete Time Parameter

  • Book
  • © 1970

Overview

Authors:
  1. K. Hinderer

    1. Institut für Mathematische Stochastik, Universität Hamburg, Hamburg, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 33)

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Table of contents (20 chapters)

  1. Front Matter

    Pages N2-VI
    Download chapter PDF

  2. Introduction and summary

    1. Introduction and summary

      • K. Hinderer
      Pages 1-4

  3. Countable state space

    1. Decision models and definition of the problem

      • K. Hinderer
      Pages 5-13

    2. The principle of optimality and the optimality equation

      • K. Hinderer
      Pages 14-27

    3. Value iteration

      • K. Hinderer
      Pages 28-29

    4. Criteria of optimality and existence of \(\bar{p} \)-optimal plans

      • K. Hinderer
      Pages 30-35

    5. Sufficient statistics, Markovian and stationary models

      • K. Hinderer
      Pages 36-47

    6. Models with incomplete information

      • K. Hinderer
      Pages 48-53

    7. Examples of special models

      • K. Hinderer
      Pages 54-62

    8. Randomized plans

      • K. Hinderer
      Pages 63-68

    9. Dynamic programming under uncertainty

      • K. Hinderer
      Pages 69-77
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Keywords

About this book

The present work is an extended version of a manuscript of a course which the author taught at the University of Hamburg during summer 1969. The main purpose has been to give a rigorous foundation of stochastic dynamic programming in a manner which makes the theory easily applicable to many different practical problems. We mention the following features which should serve our purpose. a) The theory is built up for non-stationary models, thus making it possible to treat e.g. dynamic programming under risk, dynamic programming under uncertainty, Markovian models, stationary models, and models with finite horizon from a unified point of view. b) We use that notion of optimality (p-optimality) which seems to be most appropriate for practical purposes. c) Since we restrict ourselves to the foundations, we did not include practical problems and ways to their numerical solution, but we give (cf.section 8) a number of problems which show the diversity of structures accessible to non­ stationary dynamic programming. The main sources were the papers of Blackwell (65), Strauch (66) and Maitra (68) on stationary models with general state and action spaces and the papers of Dynkin (65), Hinderer (67) and Sirjaev (67) on non-stationary models. A number of results should be new, whereas most theorems constitute extensions (usually from stationary models to non-stationary models) or analogues to known results.

Authors and Affiliations

  • Institut für Mathematische Stochastik, Universität Hamburg, Hamburg, Germany

    K. Hinderer

Bibliographic Information

  • Book Title: Foundations of Non-stationary Dynamic Programming with Discrete Time Parameter

  • Authors: K. Hinderer

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-46229-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1970

  • Softcover ISBN: 978-3-540-04956-2Published: 01 January 1970

  • eBook ISBN: 978-3-642-46229-0Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: VI, 164

  • Topics: Operations Research/Decision Theory, Operator Theory

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