Le but de ce projet s'inscrit dans le cadre de la collaboration entre Alexandre Popier, membre du Laboratoire Manceau de Mathématiques et Devin Sezer de l’Institute of Applied Mathematics, de la Middle East Technical University (METU) d’Ankara en Turquie. Cette collaboration a donné lieu à plusieurs publications et avait bénéficié d’un projet TUBITAK (équivalent de l’ANR en Turquie), entre 2018 et 2021.

Pour ce séjour, il s'agit de développer le travail initié dans notre dernière publication publiée en 2025. Celle-ci avait laissé ouvertes de nombreuses questions. Le passage de Devin en France sera l’occasion de progresser sur quelques-unes : loi de la valeur terminale (utilisation du calcul de Malliavin conditionnel), modélisation du coût terminal (avec les équations progressives-rétrogrades couplées), schémas numériques de résolution.

Since several years, Paulwin and I worked and published some articles on similar topics. Last year I was invited in Berlin to gather these competencies. Since then, Paulwin and I, together with Ulrich Horst and Guanxing Fu, we are working on the mean field game of optimal portfolio liquidation. Besides the financial application, this mean-field optimal control problem is related to a mean-field forward backward stochastic differential equation with a terminal singularity. We have obtained a first result on this topic which has been submitted very recently: solvability of the FBSDE in a new weighted integrability space, using a partial decoupling field and approximation of the Nash equilibrium. Nevertheless our requirement on the parameters of the model is quite strong, compared to the single player case. We have already raised this point during our discussions and one aim of this invitation is to enlarge the parameters setting. Until now we worked in the Brownian filtration. The second point involves working in a general filtration, for example to take into account the noise induced by the use of a dark pool for liquidation. There are also several points concerning the theory of singular BSDE we want to discuss : - asymptotic approach of GHS - existence by considering the reciprocal - existence by Perron's method / cp - uniqueness under L^\infty assumptions. This invitation is a great opportunity to develop these subjects together.