Contribution to the modeling and dynamic risk management of energy markets.

Summary This thesis is devoted to probabilistic numerical problems related to modeling, control and risk management and motivated by applications in energy markets. The main tool used is the theory of stochastic algorithms and simulation methods. This thesis consists of three parts. The first part is devoted to the estimation of two risk measures of the L-distribution of losses in a portfolio: the Value-at-Risk (VaR) and the Conditional Value-at-Risk (CVaR). This estimation is performed using a stochastic algorithm combined with an adaptive variance reduction method. The first part of this chapter deals with the case of finite dimension, the second extends the first to the case of a function of the trajectory of a process and the last one deals with the case of sequences with low discrepancy. The second chapter is dedicated to methods for hedging risk in CVaR in an incomplete market operating in discrete time using stochastic algorithms and optimal vector quantization. Theoretical results on CVaR hedging are presented and then numerical aspects are discussed in a Markovian framework. The last part is devoted to the joint modeling of spot gas and electricity prices. The multi-factor model presented is based on stationary Ornstein processes with a parametric diffusion coefficient.