Category Publications

May
2022

Ergodic control of a heterogeneous population and application to electricity pricing // Q. Jacquet, W. van Ackooij, C. Alasseur & S. Gaubert

We consider a dynamic pricing model, in which a population of customers can change contracts at any time depending on pricing conditions and customer-specific characteristics such as inertia (propensity to stay with the same supplier). A supplier then seeks to maximise its average revenue per unit time, assuming that the population is of infinite size (the 'mean field' limit). We present an application to energy pricing, and solve this problem by applying an iteration algorithm on relative values. Read more [...]

Jan
2019

Day-ahead probabilistic forecast of solar irradiance: a Stochastic Differential Equation approach - J. Badosa, E. Gobet, M. Grangereau and D. Kim

In this work, we derive a probabilistic forecast of the solar irradiance during a day at a given location, using a stochastic differential equation (SDE for short) model. We propose a procedure that transforms a deterministic forecast into a probabilistic forecast: the input parameters of the SDE model are the AROME numerical weather predictions computed at day D-1 for the day D. The model also accounts for the maximal irradiance from the clear sky model. The SDE model is mean-reverting towards Read more [...]

Dec
2018

REGRESSION MONTE CARLO FOR MICROGRID MANAGEMENT - C. ALASSEUR, A. BALATA, S. BEN AZIZA, A. MAHESHWARI, P. TANKOV AND X. WARIN

We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production to times of high demand. We build on the mathematical model introduced in [14] and optimize the diesel con-sumption under a “no-blackout” constraint. We introduce a methodology to solve microgrid man-agement problem using different variants of Read more [...]

Dec
2018

Variance optimal hedging with application to Electricity markets - Xavier Warin

In this article, we use the mean variance hedging criterion to value contracts in incomplete markets. Although the problem is well studied in a continuous and even discrete framework, very few works incorporating illiquidity constraints have been achieved and no algorithm is available in the literature to solve this problem. We first show that the valuation problem incorporating illiquidity constraints with a mean variance criterion admits a unique solution. Then we develop two Least Squares Read more [...]

Jul
2018

Estimating fast mean-reverting jumps in electricity Market models - Thomas Deschatre, Olivier Féron, and Marc Hoffmann

Based on empirical evidence of fast mean-reverting spikes, we model electricity price processes as the sum of a continuous Itö semimartingale and a a mean-reverting compound Poisson process. In a first part, we investigate the estimation of the two parameters of the Poisson process from discrete observations and establish asymptotic efficiency in various asymptotic settings. In a second part, we discuss the use of our inference results for correcting the value of forward contracts on electricity Read more [...]

Jun
2018

t and stable multivariate kernel density estimation by fast sum updating - N . Langrené, X. Warin

Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at M evaluation points given N input sample points requires a quadratic O(MN) operations, which is prohibitive for large scale problems. For this reason, approximate methods such as binning with Fast Fourier Transform or the Fast Gauss Transform have been proposed to speed up kernel density estimation. Among these fast methods, the Fast Sum Updating Read more [...]

Jun
2018

Monte Carlo for high-dimensional degenerated Semi Linear and Full Non Linear PDEs - X. Warin

We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not su er from the so called curse of dimensionality and it can be used to solve problems that were out of reach so far. We give some results of convergence and show numerically that it is effective. Besides we numerically show that the new scheme developed can be used to solve some full non linear PDEs. At last we provide an effective algorithm to implement Read more [...]

May
2017

StOpt library

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Jul
2016

Technology transition to electric mobility

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Jun
2012

Variance Optimal hedging for continuous time additive processes and applications

S. Goutte, N. Oudjane, F. Russo à paraître dans Journal of Computational Finance Juin 2012

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