Modeling and optimal strategies in short-term energy markets.

Summary This thesis focuses on providing theoretical tools to help in the development and management of intermittent renewable energy in short term electricity markets.In the first part, we develop a tractable equilibrium model for price formation in intraday electricity markets. For this, we propose a non cooperative game between several producers interacting in the market and facing an intermittent renewable production. Using stochastic control and game theory, we derive explicit optimal strategies for these producers as well as a closed form equilibrium price for different information structures and player characteristics. Our model allows to reproduce and explain the main stylized features of the intraday market such as the specific time dependence of volatility and the correlation between the price and the renewable production forecasts.In the second part, we study dynamic probabilistic forecasts in the diffusion framework. We propose several stochastic differential equation models to capture the dynamic evolution of the uncertainty associated to a forecast, derive the associated predictive densities and calibrate the model on real meteorological data. We then apply it to the problem of a wind energy producer receiving sequential updates of the probabilistic forecasts of the wind speed used to predict her production and make trading decisions in the market. We show to what extent this method can outperform the use of point forecasts in decision-making processes.Finally, in the last part, we propose to study the propertiesof aggregated shallow neural networks. We explore thePAC-Bayesian framework as an alternative to the classicalempirical risk minimization approach. We focus on Gaussianpriors and derive non-asymptotic risk bounds for theaggregated neural networks. These bounds yield minimaxrates of estimation over Sobolev smoothness classes.This analysis also provides a theoretical basis for tuning theparameters and offers new perspectives for applicationsof aggregated neural networks to practical high dimensionalproblems increasingly present in energy decision problemsinvolving renewables or storage.