Stochastic Control Methods for Optimal Portfolio Management.

Summary This thesis presents three independent research topics, the last one being declined as two distinct problems. These different topics have in common that they apply stochastic control methods to optimal portfolio management problems. In the first part, we study an asset management model that takes into account capital gains taxes. In a second part, we study a problem of detecting the maximum of a mean-reverting process. In the third and fourth parts, we look at an optimal investment problem when agents look at each other. Finally, in a fifth part, we study a variant of this problem including a penalty term instead of constraints on the admissible portfolios.