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

Author

Listed:
  • René Aïd

    (FiME Lab - Laboratoire de Finance des Marchés d'Energie - EDF R&D - EDF R&D - EDF - EDF - CREST - Université Paris-Dauphine, EDF - EDF)

  • Luciano Campi

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE ParisTech - École Nationale de la Statistique et de l'Administration Économique, LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - USPC - Université Sorbonne Paris Cité - Institut Galilée - CNRS - Centre National de la Recherche Scientifique)

  • Nicolas Langrené

    () (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Huyên Pham

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE ParisTech - École Nationale de la Statistique et de l'Administration Économique, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

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

  • René Aïd & Luciano Campi & Nicolas Langrené & Huyên Pham, 2012. "A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation," Working Papers hal-00747229, HAL.
  • Handle: RePEc:hal:wpaper:hal-00747229
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00747229
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    File URL: https://hal.archives-ouvertes.fr/hal-00747229/document
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    References listed on IDEAS

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    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.

    More about this item

    Keywords

    Optimal switching; Monte Carlo; empirical regressions; electricity market; structural model; capacity expansion;

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