IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1602.04662.html
   My bibliography  Save this paper

Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information

Author

Listed:
  • Anton A. Shardin
  • Michaela Szolgyenyi

Abstract

In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage manager and the energy price process, which is a diffusion process the drift of which is assumed to be unobservable. We apply filtering theory to find an alternative state process which is adapted to our observation filtration. For this alternative state process we derive the associated Hamilton-Jacobi-Bellman equation and solve the optimization problem numerically. This results in a candidate for the optimal policy for which it is a-priori not clear whether the controlled state process exists. Hence, we prove an existence and uniqueness result for a class of time-inhomogeneous stochastic differential equations with discontinuous drift and singular diffusion coefficient. Finally, we apply our result to prove admissibility of the candidate optimal control.

Suggested Citation

  • Anton A. Shardin & Michaela Szolgyenyi, 2016. "Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information," Papers 1602.04662, arXiv.org, revised Apr 2016.
    • Handle: RePEc:arx:papers:1602.04662
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1602.04662
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rudiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513, arXiv.org, revised Feb 2014.
    2. Zhao, Guangzhi & Davison, Matt, 2009. "Optimal control of hydroelectric facility incorporating pump storage," Renewable Energy, Elsevier, vol. 34(4), pages 1064-1077.
    3. Honda, Toshiki, 2003. "Optimal portfolio choice for unobservable and regime-switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 45-78, October.
    4. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    5. Rene Carmona & Michael Ludkovski, 2010. "Valuation of energy storage: an optimal switching approach," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 359-374.
    6. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    7. Zhuliang Chen & Peter Forsyth, 2010. "Implications of a regime-switching model on natural gas storage valuation and optimal operation," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 159-176.
    8. Matt Thompson & Matt Davison & Henning Rasmussen, 2004. "Valuation and Optimal Operation of Electric Power Plants in Competitive Markets," Operations Research, INFORMS, vol. 52(4), pages 546-562, August.
    9. Krylov, N. V. & Liptser, R., 2002. "On diffusion approximation with discontinuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 235-264, December.
    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. David Andrés‐Cerezo & Natalia Fabra, 2023. "Storing power: market structure matters," RAND Journal of Economics, RAND Corporation, vol. 54(1), pages 3-53, March.
    2. Przybyłowicz, Paweł & Szölgyenyi, Michaela & Xu, Fanhui, 2021. "Existence and uniqueness of solutions of SDEs with discontinuous drift and finite activity jumps," Statistics & Probability Letters, Elsevier, vol. 174(C).
    3. Przybyłowicz, Paweł & Szölgyenyi, Michaela, 2021. "Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 403(C).

    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. Anton A. Shardin & Michaela Szölgyenyi, 2016. "Optimal Control Of An Energy Storage Facility Under A Changing Economic Environment And Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-27, June.
    2. Abdelali Gabih & Hakam Kondakji & Jorn Sass & Ralf Wunderlich, 2014. "Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift," Papers 1402.6313, arXiv.org.
    3. Christoph Knochenhauer & Alexander Merkel & Yufei Zhang, 2024. "Optimal Investment with Costly Expert Opinions," Papers 2409.11569, arXiv.org.
    4. Jörn Sass & Dorothee Westphal & Ralf Wunderlich, 2017. "Expert Opinions And Logarithmic Utility Maximization For Multivariate Stock Returns With Gaussian Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-41, June.
    5. Jorn Sass & Dorothee Westphal & Ralf Wunderlich, 2016. "Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift," Papers 1601.08155, arXiv.org, revised Mar 2016.
    6. Michele Longo & Alessandra Mainini, 2015. "Learning and Portfolio Decisions for HARA Investors," Papers 1502.02968, arXiv.org.
    7. Nemat Safarov & Colin Atkinson, 2017. "Natural Gas-Fired Power Plants Valuation And Optimization Under Lévy Copulas And Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-38, February.
    8. Nemat Safarov & Colin Atkinson, 2016. "Natural gas-fired power plants valuation and optimisation under Levy copulas and regime-switching," Papers 1607.01207, arXiv.org, revised Jul 2016.
    9. Kristoffer Lindensjö, 2016. "Optimal investment and consumption under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 87-107, February.
    10. Kexin Chen & Hoi Ying Wong, 2022. "Duality in optimal consumption--investment problems with alternative data," Papers 2210.08422, arXiv.org, revised Jul 2023.
    11. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    12. Kexin Chen & Hoi Ying Wong, 2024. "Duality in optimal consumption–investment problems with alternative data," Finance and Stochastics, Springer, vol. 28(3), pages 709-758, July.
    13. Kristoffer Lindensjö, 2016. "Optimal investment and consumption under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 87-107, February.
    14. Michele Longo & Alessandra Mainini, 2016. "Learning And Portfolio Decisions For Crra Investors," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-21, May.
    15. Szölgyenyi Michaela, 2015. "Dividend maximization in a hidden Markov switching model," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 143-158, December.
    16. Roxana Dumitrescu & Redouane Silvente & Peter Tankov, 2024. "Price impact and long-term profitability of energy storage," Papers 2410.12495, arXiv.org.
    17. Hanfeld, Marc & Schlüter, Stephan, 2016. "Operating a swing option on today's gas markets: How least squares Monte Carlo works and why it is beneficial," FAU Discussion Papers in Economics 10/2016, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    18. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption‐Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279, April.
    19. Bastian Felix, 2012. "Gas Storage Valuation: A Comparative Simulation Study," EWL Working Papers 1201, University of Duisburg-Essen, Chair for Management Science and Energy Economics, revised Apr 2014.
    20. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1602.04662. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.