Category Publications

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 [...]

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 [...]

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 [...]

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 [...]

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 suer 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 [...]

  Read more [...]

R. Aïd, I. Ben Tahar In Commodities, Energy and Environmental Finance, ed. M. Ludkovki, R. Sircar & R. Aïd, Fields Institute Communication Series, Springer, 2015.  

L. Campi A paraître dans Musiela Festschrift, Springer Juin 2012  

I. Ekeland, A. Galichon, M. Henry à paraître dans Mathematical Finance Juin 2012 Plus d'infos.

J.-F. Chassagneux, R. Elie, I. Kharroubi à paraître dans Annals of Applied Probability Juin 2012 Plus d'infos.