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Multistage stochastic decision problems: Approximation by recursive structures and ambiguity modeling

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  • Ch. Pflug, Georg

Abstract

Stochastic multistage decision problems appear in many - if not all - application areas of Operations Research. While to define such problems is easy, to solve them is quite difficult, since they are of infinite dimension. Numerical solution can only be found by solving an approximate, easier problem. In this paper, we show good approximations can be found, where we emphasize the recursive structure of the involved algorithms and data structures.

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  • Ch. Pflug, Georg, 2023. "Multistage stochastic decision problems: Approximation by recursive structures and ambiguity modeling," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1027-1039.
    • Handle: RePEc:eee:ejores:v:306:y:2023:i:3:p:1027-1039
    DOI: 10.1016/j.ejor.2022.04.002
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    References listed on IDEAS

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    1. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
    2. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    4. Warren B. Powell, 1986. "A Stochastic Model of the Dynamic Vehicle Allocation Problem," Transportation Science, INFORMS, vol. 20(2), pages 117-129, May.
    5. Wim Ackooij & Debora Daniela Escobar & Martin Glanzer & Georg Ch. Pflug, 2020. "Distributionally robust optimization with multiple time scales: valuation of a thermal power plant," Computational Management Science, Springer, vol. 17(3), pages 357-385, October.
    6. David R. Cariño & William T. Ziemba, 1998. "Formulation of the Russell-Yasuda Kasai Financial Planning Model," Operations Research, INFORMS, vol. 46(4), pages 433-449, August.
    7. Martin Glanzer & Georg Ch. Pflug & Alois Pichler, 2017. "Incorporating statistical model error into the calculation of acceptability prices of contingent claims," Papers 1703.05709, arXiv.org, revised Jan 2019.
    8. Wim Ackooij & Debora Daniela Escobar & Martin Glanzer & Georg Ch. Pflug, 2020. "Correction to: Distributionally robust optimization with multiple time scales: valuation of a thermal power plant," Computational Management Science, Springer, vol. 17(3), pages 387-387, October.
    9. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
    10. Bita Analui & Georg Pflug, 2014. "On distributionally robust multiperiod stochastic optimization," Computational Management Science, Springer, vol. 11(3), pages 197-220, July.
    11. Santoso, Tjendera & Ahmed, Shabbir & Goetschalckx, Marc & Shapiro, Alexander, 2005. "A stochastic programming approach for supply chain network design under uncertainty," European Journal of Operational Research, Elsevier, vol. 167(1), pages 96-115, November.
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