IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v75y2020i1d10.1007_s10589-019-00135-4.html
   My bibliography  Save this article

Multiscale stochastic optimization: modeling aspects and scenario generation

Author

Listed:
  • Martin Glanzer

    (University of Vienna)

  • Georg Ch. Pflug

    (University of Vienna
    International Institute for Applied Systems Analysis (IIASA))

Abstract

Real-world multistage stochastic optimization problems are often characterized by the fact that the decision maker may take actions only at specific points in time, even if relevant data can be observed much more frequently. In such a case there are not only multiple decision stages present but also several observation periods between consecutive decisions, where profits/costs occur contingent on the stochastic evolution of some uncertainty factors. We refer to such multistage decision problems with encapsulated multiperiod random costs, as multiscale stochastic optimization problems. In this article, we present a tailor-made modeling framework for such problems, which allows for a computational solution. We first establish new results related to the generation of scenario lattices and then incorporate the multiscale feature by leveraging the theory of stochastic bridge processes. All necessary ingredients to our proposed modeling framework are elaborated explicitly for various popular examples, including both diffusion and jump models.

Suggested Citation

  • Martin Glanzer & Georg Ch. Pflug, 2020. "Multiscale stochastic optimization: modeling aspects and scenario generation," Computational Optimization and Applications, Springer, vol. 75(1), pages 1-34, January.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:1:d:10.1007_s10589-019-00135-4
    DOI: 10.1007/s10589-019-00135-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00135-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-019-00135-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Adrian S. Werner & Alois Pichler & Kjetil T. Midthun & Lars Hellemo & Asgeir Tomasgard, 2013. "Risk Measures in Multi-Horizon Scenario Trees," International Series in Operations Research & Management Science, in: Raimund M. Kovacevic & Georg Ch. Pflug & Maria Teresa Vespucci (ed.), Handbook of Risk Management in Energy Production and Trading, edition 127, chapter 0, pages 177-201, Springer.
    2. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    3. Edward Hoyle, 2010. "Information-based models for finance and insurance," Papers 1010.0829, arXiv.org.
    4. Mogens Bladt & Samuel Finch & Michael Sørensen, 2016. "Simulation of multivariate diffusion bridges," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 343-369, March.
    5. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    6. Murray Pollock, 2015. "On the Exact Simulation of (Jump) Diffusion Bridges," Papers 1505.03030, arXiv.org.
    7. Michal Kaut & Kjetil Midthun & Adrian Werner & Asgeir Tomasgard & Lars Hellemo & Marte Fodstad, 2014. "Multi-horizon stochastic programming," Computational Management Science, Springer, vol. 11(1), pages 179-193, January.
    8. G.Ch. Pflug & A. Świętanowski & E. Dockner & H. Moritsch, 2000. "The AURORA Financial Management System: Model and Parallel Implementation Design," Annals of Operations Research, Springer, vol. 99(1), pages 189-206, December.
    9. Moriggia, Vittorio & Kopa, Miloš & Vitali, Sebastiano, 2019. "Pension fund management with hedging derivatives, stochastic dominance and nodal contamination," Omega, Elsevier, vol. 87(C), pages 127-141.
    10. Flávio B. Gonçalves & Gareth O. Roberts, 2014. "Exact Simulation Problems for Jump-Diffusions," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 907-930, December.
    11. Raimund Kovacevic & Alois Pichler, 2015. "Tree approximation for discrete time stochastic processes: a process distance approach," Annals of Operations Research, Springer, vol. 235(1), pages 395-421, December.
    12. Seljom, Pernille & Tomasgard, Asgeir, 2017. "The impact of policy actions and future energy prices on the cost-optimal development of the energy system in Norway and Sweden," Energy Policy, Elsevier, vol. 106(C), pages 85-102.
    13. Holger Heitsch & Werner Römisch, 2009. "Scenario tree reduction for multistage stochastic programs," Computational Management Science, Springer, vol. 6(2), pages 117-133, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Castro, Jordi & Escudero, Laureano F. & Monge, Juan F., 2023. "On solving large-scale multistage stochastic optimization problems with a new specialized interior-point approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 268-285.
    2. Florian Ziel, 2020. "The energy distance for ensemble and scenario reduction," Papers 2005.14670, arXiv.org, revised Oct 2020.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giovanni Pantuso & Trine K. Boomsma, 2020. "On the number of stages in multistage stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 581-603, September.
    2. Francesca Maggioni & Elisabetta Allevi & Asgeir Tomasgard, 2020. "Bounds in multi-horizon stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 605-625, September.
    3. 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.
    4. Markéta Horejšová & Sebastiano Vitali & Miloš Kopa & Vittorio Moriggia, 2020. "Evaluation of scenario reduction algorithms with nested distance," Computational Management Science, Springer, vol. 17(2), pages 241-275, June.
    5. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    6. repec:uts:finphd:40 is not listed on IDEAS
    7. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2022. "Ramsey rule with forward/backward utility for long-term yield curves modeling," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 375-414, June.
    9. Ringkjøb, Hans-Kristian & Haugan, Peter M. & Nybø, Astrid, 2020. "Transitioning remote Arctic settlements to renewable energy systems – A modelling study of Longyearbyen, Svalbard," Applied Energy, Elsevier, vol. 258(C).
    10. Jan Baldeaux & Fung & Katja Ignatieva & Eckhard Platen, 2015. "A Hybrid Model for Pricing and Hedging of Long-dated Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(4), pages 366-398, September.
    11. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2013, January-A.
    12. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2019. "Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve Modeling," Post-Print hal-01721441, HAL.
    13. Kevin Fergusson & Eckhard Platen, 2014. "Hedging long-dated interest rate derivatives for Australian pension funds and life insurers," Published Paper Series 2014-7, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    14. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2018. "Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve Modeling," Working Papers hal-01721441, HAL.
    15. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007, January-A.
    16. Backe, Stian & Ahang, Mohammadreza & Tomasgard, Asgeir, 2021. "Stable stochastic capacity expansion with variable renewables: Comparing moment matching and stratified scenario generation sampling," Applied Energy, Elsevier, vol. 302(C).
    17. Huang Xiao, 2013. "Quasi-maximum likelihood estimation of multivariate diffusions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 179-197, April.
    18. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    19. Leunglung Chan & Eckhard Platen, 2016. "Pricing of long dated equity-linked life insurance contracts," Published Paper Series 2016-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    20. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 25, July-Dece.
    21. Shane Miller & Eckhard Platen, 2010. "Real-World Pricing for a Modified Constant Elasticity of Variance Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(2), pages 147-175.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:75:y:2020:i:1:d:10.1007_s10589-019-00135-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.