A probabilistic numerical method for optimal multiple switching problems in high dimension

René Aïd, Luciano Campi, Nicolas Langrené () and Huyên Pham
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René Aïd: FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CREST - EDF R&D - EDF R&D - EDF - EDF, 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 - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - 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, FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CREST - EDF R&D - EDF R&D - EDF - EDF
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 - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, 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

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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.

Keywords: Optimal switching; Monte Carlo; empirical regressions; electricity market; structural model; capacity expansion (search for similar items in EconPapers)
Date: 2012-10-30
New Economics Papers: this item is included in nep-cmp and nep-ene
Note: View the original document on HAL open archive server: https://hal.science/hal-00747229v1
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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-00747229

DOI: 10.1137/120897298

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