Contributions to credit risk and interest rate modeling.

Summary This thesis deals with several topics in financial mathematics: credit risk, portfolio optimization and interest rate modeling. Chapter 1 consists of three studies in the area of credit risk. The most innovative is the first one in which we build a model such that the immersion property is not verified under any equivalent martingale measure. Chapter 2 studies the problem of maximizing the sum of a terminal wealth utility and a consumption utility. Chapter 3 studies the valuation of interest rate derivatives in a multi-curve framework, which takes into account the difference between a risk-free rate curve and Libor rate curves of different tenors.