Charles Bertucci

Charles Bertucci

Welcome!

I am a CNRS researcher in Mathematics at the CEREMADE in Université Paris Dauphine-PSL, France. I defended my Habilitation à Diriger les Recherches in June of 2022.

I am also a part time professor at École polytechnique since 2020 and a member of the Chair Finance et développement durable funded by EDF, CACIB, Dauphine and École polytechnique.

In 2025, I have been awarded an ERC starting grant for my project PArtial DIfferential Equations on SEts of Measures, to study MFG master equations and HJB equations on sets of measures. If you have interests in these topics and are looking for thesis/PhD opportunities or organizing events, feel free to contact me.

With René Aïd, Pierre Cardaliaguet, Damien Fessler and Pierre-Louis Lions, we are organizing the workshop Mean field games and mean field control in Economics, on the 16th and 17th of December in IHP, Paris.

Download my resumé (lastly updated 2025).

Contact

Interests

Mean field games

Since my PhD thesis, I have been working on mean field games (MFG), which are basically time dependent non-atomic games (i.e. games with a lot of small players). I have a broad interest in MFG and I focused my research on i) the analysis of partial differential equations characterizing various notions of equilibria of such games, in particular the very difficult master equations, ii) applications of MFG and MFG modelling, especially in economics.

Optimal control and analysis on spaces of measures

The optimal control of systems described by a (probability) measure yields an Hamilton-Jacobi-Bellman equation on the space of measures. The problem of optimal transport typically falls in this framework. In several situations of interest, the associated Hamiltonian turns out to be quite singular and the study of the equation requires new tools, that I try to develop in the most general and useful manner.

Mathematical modelling

I have an ongoing interest for mathematical modelling, especially (but not only!) of economical situations.

Mean field systems of interacting particles

These are systems in which a large number of particles interact through a given force in such a way that the contribution of a single particle is small. Taking limits of such systems typically yields non-linear PDEs that I have been interested in, in particular for systems which are the eigenvalues of some random matrices models.

Past events

  • In 2023, I gave a Peccot Course. You can find more information here. Lecture notes of the course are available in French, and a book in English based on these notes is forthcoming.
  • With Yves Achdou, Jean-Michel Lasry and Pierre-Louis Lions, we organized the workshop Mean Field Games and Applications in 2022.

Papers

Analysis in infinite dimenion

  • [4] An approximation of the squared Wasserstein distance and an application to Hamilton-Jacobi equations, with Pierre-Louis Lions, arXiv preprint arXiv:2409.11793, 2024.
  • [3] A two spaces extension of Cauchy-Lipschitz Theorem, with Pierre-Louis Lions, arXiv preprint arXiv:2402.19092, 2024.
  • [2] Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measures, 2023, arXiv preprint arXiv:2306.04283.
  • [1] A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem, 2022 with Jean-Michel Lasry and Pierre-Louis Lions, arXiv:2210.02780, 2022.

Mean field games

  • [14] A study of common noise in mean field games, with Charles Meynard, arXiv preprint arXiv:2412.12741, 2024.

  • [13] Noise through an additional variable for mean field games master equation on finite state space, with Charles Meynard, arXiv preprint arXiv:2402.05635, 2024.

  • [12] Strategic geometric graphs through mean field games, with Matthias Rakotomalala, arXiv preprint arXiv:2404.13975, 2024.

  • [11] On Lipschitz solutions of mean field games master equation, with Jean-Michel Lasry and Pierre-Louis Lions, Journal of Functional Analysis, 287(5), 110486, 2024.

  • [10] Mean field games master equations: from discrete to continuous state space, SIAM journal on Mathematical Analysis, 56(2), 2569-2610, with Alekos Cecchin, 2024.

  • [9] Mean field games with incomplete information, 2022 pdf

  • [8] On monotone solutions of mean field games master equations Séminaire Laurent Schwartz—EDP et applications, 1-13, 2021.

  • [7] Monotone solutions for mean field games master equations: continuous state space and common noise. Communications in Partial Differential Equations, 48(10-12), 1245-1285, 2023.

  • [6] Monotone solutions for mean field games master equations: finite state space and optimal stopping. Journal de l’École polytechnique—Mathématiques, 8, 1099-1132, 2021.

  • [5] Master equation for the finite state space planning problem. Archive for Rational Mechanics and Analysis, vol. 242, p. 327-342. with J.-M. Lasry and P.-L. Lions, 2021.

  • [4] A remark on Uzawa’s algorithm and an application to mean field games systems. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 54, no 3, p. 1053-1071, 2020.

  • [3] Some remarks on mean field games. Communications in Partial Differential Equations, vol. 44, no 3, p. 205-227 with J.-M. Lasry and P.-L. Lions, 2019.

  • [2] Fokker-Planck equations of jumping particles and mean field games of impulse control. Annales de l’Institut Henri Poincaré C, Analyse non linéaire, Vol. 37. No. 5. Elsevier Masson, 2020.

  • [1] Optimal stopping in mean field games, an obstacle problem approach. Journal de Mathématiques Pures et Appliquées, Volume 120, p 165-194, 2018.

Mathematical modelling

  • [9] The equilibrium price of bubble assets, with Jean-Michel Lasry and Pierre-Louis Lions, pdf, 2025.
  • [8] Curvature in chemotaxis: A model for ant trail pattern formation, with Matthias Rakotomalala and Milica Tomasevic, arXiv preprint arXiv:2408.13363, 2024.
  • [7] Agents’ Behavior and Interest Rate Model Optimization in DeFi Lending, with Louis Bertucci, Mathis Gontier Delaunay, Olivier Gueant, and Matthieu Lesbre, available at SSRN 4802776,2024.
  • [6] A mean field model for the development of renewable capacities, with C. Alasseur, M. Basei and A. Cecchin, Mathematics and Financial Economics, 17(4), 695-719, 2023.
  • [5] How Resilient is the Bitcoin Protocol? Université Paris-Dauphine Research Paper, with L. Bertucci, J.-M. Lasry and P.-L. Lions, 2022.
  • [4] Mean Field Game Approach to Bitcoin Mining. SIAM Journal on Financial Mathematics, 15(3), 960-987, with L. Bertucci, J.-M. Lasry and P.-L. Lions, 2024.
  • [3] A class of short-term models for the oil industry addressing speculative storage. Finance and Stochastics, 26(3), 631-669, with Y. Achdou, J.-M. Lasry, P.-L. Lions, A. Rostand and J. Scheinkman, 2022.
  • [2] Strategic advantages in mean field games with a major player, Comptes Rendus Mathématique, 58.2: 113-118. with J.-M. Lasry and P.-L. Lions, 2020.
  • [1] Transmit strategies for massive machine-type communications based on mean field games. Proceedings of the International Symposium on Wireless Communication System (ISWCS), with S. Vassilaras, J.-M. Lasry, G. Paschos, M. Debbah and P.-L. Lions, 2018.

Interacting particles

  • [3] A new approach for the unitary Dyson Brownian motion through the theory of viscosity solutions, with Valentin Pesce, arXiv preprint arXiv:2504.16551, 2025.
  • [2] A spectral dominance approach to large random matrices: part II, with Jean-Michel Lasry and Pierre-Louis Lions, arXiv preprint arXiv:2402.16376, 2024.
  • [1] A spectral dominance approach to large random matrices, with Mérouane Debbah, Jean-Michel Lasry and Pierre-Louis Lions, Journal de Mathématiques Pures et Appliquées, 164, 27-56, 2022.