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

Izydorczyk Lucas (), Oudjane Nadia () and Russo Francesco ()
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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

Monte Carlo Methods and Applications, 2021, vol. 27, issue 4, 347-371

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.

Keywords: Ornstein–Uhlenbeck processes; probabilistic representation of PDEs; time-reversal of diffusion; stochastic control; HJB equation; regression Monte-Carlo scheme; demand-side management (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/mcma-2021-2095

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