Rapports de recherche

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...
01
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...
21
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....
19
Déc
2019

Numerical resolution of McKean-Vlasov FBSDEs using neural networks - Maximilien GERMAIN, Joseph MIKAEL, and Xavier WARIN

We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems. As a consequence, we obtain methods able to tackle both mean field games and mean field control problems in high dimension. We...