Credit risk models under partial information.

Summary This thesis consists of five independent parts dedicated to the modeling and study of the problems related to the risk of default, in partial information. The first part constitutes the Introduction. The second part is dedicated to the calculation of the survival probability of a firm, conditional on the information available to the investor, in a structural model with partial information. We use a hybrid numerical technique based on the Monte Carlo method and optimal quantization. In the third part we treat, with the Dynamic Programming approach, a discrete time problem of maximizing the utility of terminal wealth, in a market where securities subject to default risk are traded. The risk of contagion between defaults is modeled, as well as the possible uncertainty of the model. In the fourth part, we address the problem of uncertainty related to the investment time horizon. In a complete market subject to the risk of default, we solve, either with the martingale method or with Dynamic Programming, three problems of maximizing the utility of consumption: when the time horizon is fixed, finite but uncertain and infinite. Finally, in the fifth part we deal with a purely theoretical problem. In the context of the coarsening of filtrations, our goal is to re-demonstrate, in a specific framework, the already known results on the characterization of martingales, the decomposition of martingales with respect to the reference filtration as semimartingales in progressively and initially coarsened filtrations and the Predictable Representation Theorem.