Skip to main content
Springer Nature Link
Log in

Algorithmic Aspects of Scenario-Based Multi-stage Decision Process Optimization

  • Conference paper
Algorithmic Decision Theory (ADT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5783))

Included in the following conference series:

  • 1118 Accesses

Abstract

Multi-stage decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future uncertain values on which the decision will depend on. The quality of the scenario model severely affects the quality of the solution of the optimization model. Various approaches towards an optimal generation of discrete-state approximations (represented as scenario trees) have been suggested in the literature. Direct scenario tree sampling based on historical data or econometric models, as well as scenario path simulation and optimal tree approximation methods are discussed from an algorithmic perspective. A multi-stage financial asset management decision optimization model is presented to outline strategies to analyze the impact of various algorithmic scenario generation methodologies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Eichhorn, A., Römisch, W.: Polyhedral risk measures in stochastic programming. SIAM Journal on Optimization 16(1), 69–95 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ruszczyński, A., Shapiro, A. (eds.): Stochastic programming. Handbooks in Operations Research and Management Science, vol. 10. Elsevier Science B.V., Amsterdam (2003)

    MATH  Google Scholar 

  3. Wallace, S.W., Ziemba, W.T. (eds.): Applications of stochastic programming. MPS/SIAM Series on Optimization, vol. 5. Society for Industrial and Applied Mathematics, SIAM (2005)

    Google Scholar 

  4. Dupačová, J., Consigli, G., Wallace, S.W.: Scenarios for multistage stochastic programs. Annals of Operations Research 100, 25–53 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Pennanen, T.: Epi-convergent discretizations of multistage stochastic programs. Mathematics of Operations Research 30(1), 245–256 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kuhn, D.: Aggregation and discretization in multistage stochastic programming. Mathematical Programming 113(1, Ser. A), 61–94 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hilli, P., Pennanen, T.: Numerical study of discretizations of multistage stochastic programs. Kybernetika 44(2), 185–204 (2008)

    MathSciNet  MATH  Google Scholar 

  8. Kaut, M., Wallace, S.W.: Evaluation of scenario generation methods for stochastic programming. Pacific Journal of Optimization 3(2), 257–271 (2007)

    MathSciNet  MATH  Google Scholar 

  9. Markowitz, H.M.: Portfolio selection. The Journal of Finance 7(1), 77–91 (1952)

    Google Scholar 

  10. Hochreiter, R.: Evolutionary stochastic portfolio optimization. In: Brabazon, A., ONeill, M. (eds.) Natural Computing in Computational Finance. Studies in Computational Intelligence, vol. 100, pp. 67–87. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Mathematical Finance 9(3), 203–228 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Steinbach, M.C.: Markowitz revisited: mean-variance models in financial portfolio analysis. SIAM Review 43(1), 31–85 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rockafellar, R., Uryasev, S.: Optimization of Conditional Value-at-Risk. The Journal of Risk 2(3), 21–41 (2000)

    Article  Google Scholar 

  14. Casey, M.S., Sen, S.: The scenario generation algorithm for multistage stochastic linear programming. Mathematics of Operations Research 30(3), 615–631 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Høyland, K., Wallace, S.W.: Generating scenario trees for multistage decision problems. Management Science 47(2), 295–307 (2001)

    Article  MATH  Google Scholar 

  16. Rachev, S.T., Römisch, W.: Quantitative stability in stochastic programming: the method of probability metrics. Mathematics of Operations Research 27(4), 792–818 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Heitsch, H., Römisch, W., Strugarek, C.: Stability of multistage stochastic programs. SIAM Journal on Optimization 17(2), 511–525 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Pflug, G.C.: Scenario tree generation for multiperiod financial optimization by optimal discretization. Mathematical Programming 89(2, Ser. B), 251–271 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  19. Dupačová, J., Gröwe-Kuska, N., Römisch, W.: Scenario reduction in stochastic programming. An approach using probability metrics. Mathematical Programming 95(3, Ser. A), 493–511 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pennanen, T., Koivu, M.: Epi-convergent discretizations of stochastic programs via integration quadratures. Numerische Mathematik 100(1), 141–163 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Koivu, M.: Variance reduction in sample approximations of stochastic programs. Mathematical Programming 103(3, Ser. A), 463–485 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Pennanen, T.: Epi-convergent discretizations of multistage stochastic programs via integration quadratures. Mathematical Programming 116(1-2, Ser. B), 461–479 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Topaloglou, N., Vladimirou, H., Zenios, S.: Cvar models with selective hedging for international asset allocation. Journal of Banking and Finance 26(7), 1535–1561 (2002)

    Article  Google Scholar 

  24. Hochreiter, R., Pflug, G.C.: Financial scenario generation for stochastic multi-stage decision processes as facility location problems. Annals of Operations Research 152(1), 257–272 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Decision Support Systems, University of Vienna, Vienna, Austria

    Ronald Hochreiter

Authors
  1. Ronald Hochreiter
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Padova, Via Trieste 63, 35121, Padova, Italy

    Francesca Rossi

  2. LAMSADE-CNRS, University of Paris Dauphine, Place du Maréchal De Lattre de Tassigny, 75775, Paris Cedex 16, France

    Alexis Tsoukias

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hochreiter, R. (2009). Algorithmic Aspects of Scenario-Based Multi-stage Decision Process Optimization. In: Rossi, F., Tsoukias, A. (eds) Algorithmic Decision Theory. ADT 2009. Lecture Notes in Computer Science(), vol 5783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04428-1_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04428-1_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04427-4

  • Online ISBN: 978-3-642-04428-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics