Category Rapports

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 surcroit des données privées), on souhaiterait piloter Read more [...]

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 consommateurs ont la forme d’un jeu stochastique non-coopératif à somme non-nulle qui, lorsque ces Read more [...]

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 falls (-40%) resulting in revenue losses of 1.2 billion € (-45%) for market participants. This paper argues that Read more [...]

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 the population. Therefore, the government can put into place incentive policies to encourage the lockdown of the population. In addition, the government may Read more [...]

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 (weather). Agents production capacities are subject to independent random outages, which are each modelled Read more [...]

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 by neural networks through sequential minimizations of suitable quadratic loss functions that are performed Read more [...]

Juil
2020

Fast multivariate empirical cumulative distribution function with connection to kernel density estimation - Nicolas Langrené & Xavier Warin

This paper revisits the problem of computing empirical cumulative distribution functions (ECDF) efficiently on large, multivariate datasets. Computing an ECDF at one evaluation point requires O(N) operations on a dataset composed of N data points. Therefore, a direct evaluation of ECDFs at N evaluation points requires a quadratic O(N^2) operations, which is prohibitive for large-scale problems. Two fast and exact methods are proposed and compared. The first one is based on fast summation in lexicographical Read more [...]

Juil
2020

Reaching New Lows? The Pandemic's Consequences for Electricity Markets - David Benatia

The large reductions in electricity demand caused by the COVID-19 crisis have disrupted electricity systems worldwide. This article draws insights from New York into the consequences of the pandemic for electricity markets. It disentangles the e ffects of the demand reductions, increased forecast errors, and fuel price drops on the day-ahead and real-time markets. From March 16 to May 31, New York has experienced a 6.5% demand reduction, prices have dropped, and producers have lost $87 million (-18%). Read more [...]

Juil
2020

Estimation of the number of factors in a multi-factorial Heath-Jarrow-Morton model in electricity markets - Olivier Féron & Pierre Gruet

In this paper we study the calibration of specific multi-factorial Heath-Jarrow-Morton models to electricity market prices, with a focus on the estimation of the optimal number of factors. We describe a common statistical procedure based on likelihood maximisation and Akaike / Bayesian information criteria, in the case of calibration on futures prices, as well as on both spot and futures prices. We perform a detailed analysis on 6 European markets: Belgium, France, Germany, Italy, Switzerland and Read more [...]

Avr
2020

A Principal-Agent approach to study Capacity Remuneration Mechanisms - Clémence Alasseur, Heythem Farhat and Marcelo Saguan

We propose to study electricity capacity remuneration mechanism design through a Principal-Agent approach. The Principal represents the aggregation of electricity consumers (or a representative entity), subject to the physical risk of shortage, and the Agent represents the electricity capacity owners, who invest in capacity and produce electricity to satisfy consumers’ demand, and are subject to financial risks. Following the methodology of Cvitanic et al. (2017), we propose an optimal contract, Read more [...]

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