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The project Caesars is granted by the Agence Nationale de la Recherche for years 2016-2018. The acronym Caesars is related to Control and simulAtion of Electrical Systems, interAction and RobustnesS. The three partners are Ecole Polytechnique, Université du Maine and Electricité de France.
In electrical system, strong evolutions are under way that will change deeply the organisation of the whole sector in the short and long term horizon: quick development of renewable technology, volatile and unpredictable production, costly investments in a difficult economic context, competing environment, emission market, new usages of electric vehicles... The simulation and analysis of the evolution of the electrical system is fundamental for better sustaining the energetic transition to a Clean Energy World but it is challenging because of various sources of uncertainties and their interdependence, the interaction between actors and between decisions. Our aim is to develop simplified mathematical models, based on stochastic controls and differential games models, together with the numerical method apparatus to address important problems related to optimal investment, renewable subvention policy, portfolio management, pricing policy of power companies, stress-testing, among others.

Latest news


The research team of the Caesars project is publishing their results in international reviews. Preprints are regularly added on this site and can be downloaded. [more]


Software of the published results are available on this site.[more]


Academic and private researchers compose the team of the Caesars project. The three partners are Ecole Polytechnique, Université du Maine and Electricité de France. [more]


For more information on the project, please contact us.


  • N. Baradel, B. Bouchard and N. M. Dang, Optimal control under uncertainty and Bayesian parameters adjustments [Arxiv].
  • E. Bayraktar, A. Cosso, H. Pham, Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics [Hal].
  • G. Fort, E. Gobet and E. Moulines, MCMC design-based non-parametric regression for rare-event. Application to nested risk computations [Hal].
  • E. Gobet, G. Liu and J. Zubelli, A non-intrusive stratified resampler for regression Monte-Carlo: application to solving non-linear equations [Hal].
  • E. Gobet and S. Pagliarani, Analytical approximations of non-linear SDEs of McKean-Vlasov type [Hal].
  • H. Pham, Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications [Hal]
  • H. Pham and X. Wei, Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics [Hal].


  • StOpt: STochastic OPTimization library in C++ with a Python wrapper.

  • The STochastic OPTimization library (StOpt) aims at providing tools in C++ for solving some stochastic optimization problems encountered in finance or in the industry. A python binding is available for some C++ objects provided permitting to easily solve an optimization problem by regression. Different methods are available: dynamic drogramming methods based on Monte Carlo with regressions, Semi-Lagrangian methods for Hamilton Jacobi Bellman general equations, stochastic dual dynamic programming methods.
  • For each method, a framework is provided to optimize the problem and then simulate it out of the sample using the optimal commands previously calculated. Parallelization methods based on OpenMP and MPI are provided in this framework permitting to solve high dimensional problems on clusters. The library should be flexible enough to be used at different levels depending on the user's willingness.

  • Git repository:
  • Documentation:


Membres permaments Postdoctorants et ingénieurs Doctorants et stagiaires

Aid René, Université Paris-Dauphine Basei Matteo, Université Paris 7 Grangereau Maxime, École Polytechnique
Allasseur Clémence, Electricité de France Francisco Bernal, École Polytechnique Liu Gang, École Polytechnique
Ben Tahar Imen, Université Paris-Dauphine Lenôtre Lionel, École Polytechnique Pimentel Isaque, Électricité de France
Bion-Nadal Jocelyne, CNRS - École Polytechnique
Bouchard Bruno, Université Paris-Dauphine
Brouste Alexandre, Université du Maine
Buckdahn Rainer, Université de Bretagne Occidentale
Denis Laurent, Université du Maine
Gobet Emmanuel, Ecole Polytechnique
Hu Ying, Université Rennes 1
Matoussi Anis, Université du Maine
Pham Huyen, Université Paris 7
Warin Xavier, Electricité de France7