École Nationale Supérieure de
Techniques Avancées

Résumé

The report will begin by presenting fundamental concepts that are essential for modelling the ETS. It will start with an overview of the Mean Field Theory, that enables treating two different categories of problems: the mean field gamed and the mean field control problems. Then, the concept of forward-backward stochastic differential equation (FBSDE) will be introduced, as it is used to determine the behaviour of a market actor. This will be followed by an exploration of different market modelling through the existing literature on the subject. It will provide a good understanding of how a market, whatever its nature, can be mathematically understood. Finally, the chosen model for the ETS will be presented in order to implement it. This will allow a discussion of the different parameters the regulator can control and how they may affect the market.