MFG / Center Lagrange: The HJB / MFG models for ALM under state constraints and the management of scarce resources in bank balance sheets associated with new regulatory constraints

Scientific project

The Institut Louis Bachelier is committed, within the framework of agreements with its clients, to contribute to fundamental exploratory and collaborative research, with the objective that this research draws avenues of scientific work in the perspective of the creation of a new Institute for fundamental and applied research in mathematics oriented towards fields likely to advance fundamental mathematical knowledge likely to have an impact in new information and communications technologies (NICT).

Fundamental research on state-constrained MFG systems, found in ALM management banking networks, fits naturally into this context. Indeed, these state constraints make it possible to integrate the management of scarce resources which can also be applied to ICT networks.

In this context, many questions arise. One of the main challenges is to protect the system while leaving room for maneuver to the various players so as to allow competition to operate with expected optimization effects.

The mathematical and fundamental tools of the HJB theory of stochastic control and of the MFG theory under state constraints are poorly developed and this research project aims to improve the analytical and numerical processing of these couplings / MFG.

The IEF as a Research Foundation, provides the appropriate and necessary framework for fundamental research with the objective of advancing scientific knowledge, and has the capacity and attractiveness necessary to mobilize advanced academic skills of the highest level. necessary for this fundamental research leading to scientific publications.

The ILB therefore wishes to entrust a research mission to the IEF on “HJB / MFG models for ALM under state constraints and the management of scarce resources in bank balance sheets associated with new regulatory constraints”.

The mission of the IEF is to carry out the research project:

“The HJB / MFG models for ALM under state constraints and the management of scarce resources from bank balance sheets associated with new regulatory constraints”; ensure the scientific publication of the results obtained: an article published in a mathematical journal, and send the ILB a research report on the research carried out, the results obtained, the new avenues opened up by this work, the follow-up possible and expected outcomes.

The IEF must therefore:

• Bring together the scientific skills likely to carry out this research,
• Pilot the research work program to carry out this project,
• Ensure the achievement of the deliverables indicated above.