A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems-Reference-Cited by-同舟云学术

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

Published:2021-10-21 Issue:4 Volume:27 Page:347-371
ISSN:0929-9629
Container-title:Monte Carlo Methods and Applications
language:en
Short-container-title:

Author:

Izydorczyk Lucas¹,Oudjane Nadia²,Russo Francesco¹

Affiliation:

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

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

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Statistics and Probability

Link

https://www.degruyter.com/document/doi/10.1515/mcma-2021-2095/pdf

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