Rapports de recherche

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...
01
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...
01
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...