Rapports de recherche

09
Mar
2021

Decomposition of High Dimensional Aggregative Stochastic Control Problems - A. Seguret, C. Alasseur, J. F. Bonnans, A. De Paola, N. Oudjane, V. Trovato

Coordonner à grande échelle le fonctionnement des appareils électriques « flexibles » (typiquement régulés par thermostat) des particuliers est crucial pour assurer l’équilibrage de réseaux électriques qui sont de plus en plus alimentés par des sources renouvelables, par nature intermittentes. Parce qu’un pilotage centralisé de ces flexibilités nécessiterait l’échange de grandes quantités d’information (qui seraient de...
27
Jan
2021

MFG model with a long-lived penalty at random jump times: application to demand side management for electricity contracts - C. Alasseur, L. Campi, R. Dumitrescu, J. Zeng

L'article cherche à décrire la dynamique collective d’un marché de fourniture d’électricité dans lequel une fraction des consommateurs ont souscrit un contrat de type « demand side management », contrat par lequel ils s’engagent à réduire leur consommation pendant des durées prédéterminée et à des instants qui leur sont indiqués de manière aléatoire. Les interactions entre...
18
Nov
2020

Ring the Alarm! Electricity Markets, Renewables, and the Pandemic - David Benatia

The pandemic's impacts on European electricity markets have been enormous, especially in countries with abundant near-zero marginal cost of production like France. This article provides an in-depth quantitative study of the impacts of the crisis on the French electricity sector. During the lockdown episode, France has experienced unparalleled demand reductions (-11.5%) and energy price...
18
Nov
2020

Incentives, lockdown, and testing : from Thucydides’s Analysis to the COVID-19 pandemie - E. Hubert, T. Mastrolia, D. Possamaï and X. Warin

We consider the control of the COVID–19 pandemic via incentives, through either stochastic SIS or SIR compartmental models. When the epidemic is ongoing, the population can reduce interactions between individuals in order to decrease the rate of transmission of the disease, and thus limit the epidemic. However, this effort comes at a cost for...
13
Nov
2020

Equilibrium price in intraday electricity markets - René Aid, Andrea Cosso, and Huyên Pham

We formulate an equilibrium model of intraday trading in electricity markets. Agents face balancing constraints between their customers consumption plus intraday sales and their production plus intraday purchases. They have continuously updated forecast of their customers consumption at maturity with decreasing volatility error. Forecasts are prone to idiosyncratic noise as well as common noise...
01
Juil
2020

Deep backward multistep schemes for nonlinear PDEs and approximation error analysis - M. Germain, H. Pham & X. Warin

We develop multistep machine learning schemes for solving nonlinear partial differential equations (PDEs) in high dimension. The method is based on probabilistic representation of PDEs by backward stochastic differential equations (BSDEs) and its iterated time discretization. In the case of semilinear PDEs, our algorithm estimates simultaneously by backward induction the solution and its gradient...