Our aim is to develop together with our industrial partner EDF numerical and theoretical tools which are essential for decision making in a random environment related with the ecological transition. For this we propose to develop simplified mathematical models together with numerical methods, in order to give an answer to major applications, as for example : + The problems of storage related with the development of renewable energies ; + The development of decision tools in a context of ecological transition and decarbonisation ; + The need of dynamic investment models in a competitive environment with different energy producers ; + The risk management in extreme situations and with many risk factors. In our approach our expertise in developing efficient numerical methods in stochastic control, in stochastic and mean-field games as well as for models with uncertainty, combined with the practical expertise of EDF will be crucial, to produce understandable results which can then be used as a guide for efficient public and utilities decisions. Backward stochastic differential equations (BSDE) are a powerful tool of control, known and also already tested by EDF R&D. Related with the problems explained above, our objective consists in the study of efficient algorithms for BSDE in high dimension as required by applications, and to enlarge the class of control problems which can be considered with. The dynamic modelling of investment in a competitive environment is related with the study of stochastic games, and in the case of a large number of agents, with mean-field games. We will focus on investment games in which the agents have different objectives. A major problem for the games will be to develop a suitable notion of equilibrium, while for the mean-field games our objective is to include in the model a control of the local risk. Accounting for extreme situations in the Decision-Making tools constitutes another original aspect of the project. Our aim is also to develop methodologies to assess and measure extremes risks, identify and anticipate critical situations, by using the technics of rare events. We integrate extreme risks in the resolution of stochastic control problems. Moreover, as industrial and societal issues concern several decades, the stochastic model and the optimisation criteria are imperfectly identified, the uncertainty of the risk modelling is large. We tackle these issues by following two ways: first, using a « worst case » approach, using the theory of decision robustness. Second, with the quantification of uncertainty and sensitivity analysis. The research objectives of the project are not only of great interest for EDF but also for any company having to take decisions for a long time horizon, with a large number of variables or with model uncertainty, which is the case for sectors related with energy. Our research programme is split into the following milestones, which are transversal to the major applications aforementioned: Task 1. BSDE-based efficient algorithms for optimal stochastic control ; Task 2. Stochastic and mean-field games ; Task 3. Rare event analysis in optimal decision and risk management ; Task 4. Sensitivity analysis, The research results obtained in the frame of the project will be disseminated by publication in international journals with referee system, by a summer school and a conference, but also by the development of a public bank of benchmark problems and by making available the open-source codes of the developed programs.