Advertisement

Dynamic Stochastic Optimization

  • Kurt Marti
  • Yuri Ermoliev
  • Georg Pflug
Conference proceedings

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 532)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Dynamic Decision Problems under Uncertainty: Modeling Aspects

    1. Front Matter
      Pages 1-1
    2. Peter Kall, János Mayer
      Pages 21-41
    3. Julien Granger, Ananth Krishnamurthy, Stephen M. Robinson
      Pages 67-79
  3. Dynamic Stochastic Optimization in Finance

    1. Front Matter
      Pages 81-81
    2. Vadim I. Arkin, Alexander D. Slastnikov
      Pages 83-98
    3. Stephen W. Bianchi, Roger J-B Wets, Liming Yang
      Pages 99-114
    4. M. A. H. Dempster, M. Germano, E. A. Medova, M. Villaverde
      Pages 115-130
  4. Optimal Control Under Stochastic Uncertainty

  5. Tools for Dynamic Stochastic Optimization

About these proceedings

Introduction

Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic­ itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec­ tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci­ sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu­ tions. Objective and constraint functions of dynamic stochastic optimization problems have the form of multidimensional integrals of rather involved in­ that may have a nonsmooth and even discontinuous character - the tegrands typical situation for "hit-or-miss" type of decision making problems involving irreversibility ofdecisions or/and abrupt changes ofthe system. In general, the exact evaluation of such functions (as is assumed in the standard optimization and control theory) is practically impossible. Also, the problem does not often possess the separability properties that allow to derive the standard in control theory recursive (Bellman) equations.

Keywords

Analysis Stochastic Decision Processes Stochastic Networks Stochastic Optimization Stochastic Programming optimal control optimization

Editors and affiliations

  • Kurt Marti
    • 1
  • Yuri Ermoliev
    • 2
  • Georg Pflug
    • 3
  1. 1.Aero-Space Engineering and TechnologyFederal Armed Forces University MunichNeubiberg/MunichGermany
  2. 2.IIASA LaxenburgLaxenburg/WienAustria
  3. 3.Institute of Statistics and Decision Support Systems (ISDS)University of WienWienAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-55884-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-40506-1
  • Online ISBN 978-3-642-55884-9
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site