Some estimation and optimal control problems for stochastic processes in an electricity market price modeling framework.

Summary This thesis deals with the study of mathematical models of price movements in electricity markets, from the point of view of process statistics and stochastic optimal control. In the first part, we estimate the volatility components of a multidimensional diffusion process representing the evolution of prices on the electricity futures market. Its dynamics is driven by two Brownian motions. We seek to perform the estimation efficiently in terms of speed of convergence, and limit variance with respect to the parametric part of these components. This requires an extension of the usual definition of efficiency in the Cramér-Rao sense. Our estimation methods are based on the realized quadratic variation of the observed process. In the second part, we add model error terms to the observations of the previous model, to overcome the problem of overdetermination that arises when the dimension of the observed process is greater than two. The estimation techniques are still based on the realized quadratic variation, and we propose other tools to continue estimating the volatility components with the optimal speed in the presence of the error terms. Numerical tests are used to highlight the presence of such errors in our data. Finally, in the last part we solve the problem of a producer who intervenes on the intraday electricity market in order to compensate for the costs related to the random returns of his production units. Through his actions, he has an impact on the market. The prices and its anticipation of the demand of its consumers are modeled by a jumping diffusion. The tools of stochastic optimal control allow us to determine his strategy in an approximate problem. We give conditions for this strategy to be very close to optimality in the initial problem, and illustrate it numerically.