My research lies at the intersection of optimal control, optimal transport, calculus of variations, and partial differential equations. I am particularly interested in mean-field games, a modern framework that models strategic decision-making in large populations by approximating Nash equilibria through the lens of mean-field theory.
My earlier work focused on price-formation models in mean-field games, which involve the standard value function and density and an evolving price variable. I explored these models using a variety of analytical and numerical techniques.
More recently, I have extended my work to mean-field games of optimal stopping, introducing new mathematical challenges and practical implications in energy policy and stochastic decision-making.
I am motivated by the rich interplay between theory and application, and by the opportunity to develop tools that offer insights into complex systems governed by strategic interaction and uncertainty.
Roxana Dumitrescu, Julian G. Pineda, and Peter Tankov. Two-scale mean-field games with common noise, 2024.
Roxana Dumitrescu, Julian G. Pineda, and Peter Tankov. Machine learning approach to day-ahead energy price generation, 2024.
We introduce the so-called potential approach for the deterministic price-formation mean-field game model. Using Poincaré Lemma, we obtain a variational problem for a single function (instead of the original three). Our approach relies on the calculus of variations theory.
We extend the machine learning-based approach introduced in our previous work to include the price formation problem with common noise, using a posteriori estimates to guarantee convergence.
We use machine learning to solve the deterministic price-formation mean-field games model numerically. We develop a posteriori estimates to guarantee the training's convergence. Our approach relies on the calculus of variations theory and recurrent neural networks.
We consider the finite players' game with common noise and its mean-field limit. The price arises as a Lagrange multiplier of a market-clearing condition. Our approach relies on the calculus of variations theory.
We merge the potential approach and machine learning methods to solve the deterministic and stochastic mean-field game price formation models. Our approach relies on the (stochastic) calculus of variations theory and recurrent neural networks.
We study the deterministic price formation problem using the Aubry-Mather theory. We obtain a variational problem on a space of measures. Our approach relies on the optimal transport (duality) theory.
We propose the stochastic version (common noise) of the price-formation mean-field game model introduced by Gomes & Saúde in the deterministic setting. Our approach relies on the optimal control theory.