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A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems

Author

Listed:
  • Izydorczyk Lucas

    (ENSTA Paris, Institut Polytechnique de Paris, Unité de Mathématiques Appliquées (UMA), Palaiseau, France)

  • Oudjane Nadia

    (EDF R&D; and FiME (Laboratoire de Finance des Marchés de l’Energie (Dauphine, CREST, EDF R&D)), Palaiseau, France)

  • Russo Francesco

    (ENSTA Paris, Institut Polytechnique de Paris, Unité de Mathématiques Appliquées (UMA), Palaiseau, France)

Abstract

We propose a fully backward representation of semilinear PDEs with application to stochastic control. Based on this, we develop a fully backward Monte-Carlo scheme allowing to generate the regression grid, backwardly in time, as the value function is computed. This offers two key advantages in terms of computational efficiency and memory. First, the grid is generated adaptively in the areas of interest, and second, there is no need to store the entire grid. The performances of this technique are compared in simulations to the traditional Monte-Carlo forward-backward approach on a control problem of thermostatic loads.

Suggested Citation

  • Izydorczyk Lucas & Oudjane Nadia & Russo Francesco, 2021. "A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems," Monte Carlo Methods and Applications, De Gruyter, vol. 27(4), pages 347-371, December.
    • Handle: RePEc:bpj:mcmeap:v:27:y:2021:i:4:p:347-371:n:1
    DOI: 10.1515/mcma-2021-2095
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