IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1210.8175.html
   My bibliography  Save this paper

A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation

Author

Listed:
  • Ren'e Aid

    (FiME Lab)

  • Luciano Campi

    (CREST, LAGA)

  • Nicolas Langren'e

    (LPMA)

  • Huy^en Pham

    (CREST, LPMA)

Abstract

In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the size of the local hypercubes involved in the regressions, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants. This model takes into account electricity demand, cointegrated fuel prices, carbon price and random outages of power plants. It computes the optimal level of investment in each generation technology, considered as a whole, w.r.t. the electricity spot price. This electricity price is itself built according to a new extended structural model. In particular, it is a function of several factors, among which the installed capacities. The evolution of the optimal generation mix is illustrated on a realistic numerical problem in dimension eight, i.e. with two different technologies and six random factors.

Suggested Citation

  • Ren'e Aid & Luciano Campi & Nicolas Langren'e & Huy^en Pham, 2012. "A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation," Papers 1210.8175, arXiv.org.
    • Handle: RePEc:arx:papers:1210.8175
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1210.8175
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    2. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    3. Connolly, D. & Lund, H. & Mathiesen, B.V. & Leahy, M., 2010. "A review of computer tools for analysing the integration of renewable energy into various energy systems," Applied Energy, Elsevier, vol. 87(4), pages 1059-1082, April.
    4. Grégory Benmenzer & Emmanuel Gobet & Céline Jérusalem, 2007. "Arbitrage free cointegrated models in gas and oil future markets," Working Papers hal-00200422, HAL.
    5. Walter Schachermayer & Josef Teichmann, 2007. "How close are the option pricing formulas of Bachelier and Black-Merton-Scholes?," Papers 0711.1272, arXiv.org.
    6. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    7. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    8. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    9. Hobbs, Benjamin F., 1995. "Optimization methods for electric utility resource planning," European Journal of Operational Research, Elsevier, vol. 83(1), pages 1-20, May.
    10. repec:cdl:anderf:qt43n1k4jb is not listed on IDEAS
    11. Bar-Ilan, Avner & Sulem, Agnes & Zanello, Alessandro, 2002. "Time-to-build and capacity choice," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 69-98, January.
    12. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    13. René Aïd & Luciano Campi & Adrien Nguyen Huu & Nizar Touzi, 2009. "A Structural Risk-Neutral Model Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 925-947.
    14. Felipe L. Aguerrevere, 2003. "Equilibrium Investment Strategies and Output Price Behavior: A Real-Options Approach," The Review of Financial Studies, Society for Financial Studies, vol. 16(4), pages 1239-1272.
    15. Kerry Back & Dirk Paulsen, 2009. "Open-Loop Equilibria and Perfect Competition in Option Exercise Games," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4531-4552, November.
    16. Foley, A.M. & Ó Gallachóir, B.P. & Hur, J. & Baldick, R. & McKeogh, E.J., 2010. "A strategic review of electricity systems models," Energy, Elsevier, vol. 35(12), pages 4522-4530.
    17. Gr'egory Benmenzer & Emmanuel Gobet & C'eline J'erusalem, 2007. "Arbitrage free cointegrated models in gas and oil future markets," Papers 0712.3537, arXiv.org.
    18. Frederic H. Murphy & Yves Smeers, 2005. "Generation Capacity Expansion in Imperfectly Competitive Restructured Electricity Markets," Operations Research, INFORMS, vol. 53(4), pages 646-661, August.
    19. Dyner, Isaac & Larsen, Erik R., 2001. "From planning to strategy in the electricity industry," Energy Policy, Elsevier, vol. 29(13), pages 1145-1154, November.
    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. Ben Zineb Tarik & Gobet Emmanuel, 2013. "Preliminary control variates to improve empirical regression methods," Monte Carlo Methods and Applications, De Gruyter, vol. 19(4), pages 331-354, December.

    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. René Aïd & Luciano Campi & Nicolas Langrené & Huyên Pham, 2012. "A probabilistic numerical method for optimal multiple switching problems in high dimension," Working Papers hal-00747229, HAL.
    2. Aïd, René & Campi, Luciano & Langrené, Nicolas & Pham, Huyên, 2014. "A probabilistic numerical method for optimal multiple switching problems in high dimension," LSE Research Online Documents on Economics 63011, London School of Economics and Political Science, LSE Library.
    3. Fredrik Armerin & Han-Suck Song, 2021. "A framework for modelling cash flow lags," SN Business & Economics, Springer, vol. 1(10), pages 1-13, October.
    4. GAHUNGU, Joachim & SMEERS, Yves, 2011. "A real options model for electricity capacity expansion," LIDAM Discussion Papers CORE 2011044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Chevalier-Roignant, Benoît & Flath, Christoph M. & Huchzermeier, Arnd & Trigeorgis, Lenos, 2011. "Strategic investment under uncertainty: A synthesis," European Journal of Operational Research, Elsevier, vol. 215(3), pages 639-650, December.
    6. Joachim Gahungu and Yves Smeers, 2012. "A Real Options Model for Electricity Capacity Expansion," RSCAS Working Papers 2012/08, European University Institute.
    7. Chevalier-Roignant, Benoît & Flath, Christoph M. & Kort, Peter M. & Trigeorgis, Lenos, 2021. "Capacity investment choices under cost heterogeneity and output flexibility in oligopoly," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1154-1173.
    8. Jeon, Haejun, 2024. "The effects of time-to-build and regulation on investment timing and size," International Review of Financial Analysis, Elsevier, vol. 96(PB).
    9. Igor V. Kravchenko & Cláudia Nunes & Carlos Oliveira, 2023. "Investment in two alternative projects with multiple switches and the exit option," Mathematics and Financial Economics, Springer, volume 17, number 1, December.
    10. Masci, Martín Ezequiel, 2012. "Irreversibilidad e incertidumbre de las decisiones financieras en i&d [Irreversibility and uncertainty of the financial investments on r&d]," MPRA Paper 40970, University Library of Munich, Germany.
    11. Haas, J. & Cebulla, F. & Cao, K. & Nowak, W. & Palma-Behnke, R. & Rahmann, C. & Mancarella, P., 2017. "Challenges and trends of energy storage expansion planning for flexibility provision in low-carbon power systems – a review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 603-619.
    12. Li, Xishu & Zuidwijk, Rob & de Koster, M.B.M, 2023. "Optimal competitive capacity strategies: Evidence from the container shipping market," Omega, Elsevier, vol. 115(C).
    13. Michael Ludkovski, 2010. "Stochastic Switching Games and Duopolistic Competition in Emissions Markets," Papers 1001.3455, arXiv.org, revised Aug 2010.
    14. Hans Haanappel & Han Smit, 2007. "Return distributions of strategic growth options," Annals of Operations Research, Springer, vol. 151(1), pages 57-80, April.
    15. Kuno J.M. Huisman & Peter M. Kort, 2015. "Strategic capacity investment under uncertainty," RAND Journal of Economics, RAND Corporation, vol. 46(2), pages 376-408, June.
    16. Smit, Han T.J. & Trigeorgis, Lenos, 2006. "Real options and games: Competition, alliances and other applications of valuation and strategy," Review of Financial Economics, Elsevier, vol. 15(2), pages 95-112.
    17. Roques, Fabien A. & Savva, Nicos, 2009. "Investment under uncertainty with price ceilings in oligopolies," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 507-524, February.
    18. Marrero-Trujillo, Verónica & Arias-Gaviria, Jessica & Arango-Aramburo, Santiago & Larsen, Erik R., 2023. "Gamification model for communicating and evaluating renewable energy planning," Utilities Policy, Elsevier, vol. 84(C).
    19. Bobtcheff, Catherine & Villeneuve, Stéphane, 2010. "Technology choice under several uncertainty sources," European Journal of Operational Research, Elsevier, vol. 206(3), pages 586-600, November.
    20. Aïd, René & Federico, Salvatore & Pham, Huyên & Villeneuve, Bertrand, 2015. "Explicit investment rules with time-to-build and uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 240-256.

    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:1210.8175. 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.