Some contributions to risk control in mathematical finance.

Summary The first part of this thesis deals with vector risk measures. In Chapter 1, we generalize the notion of a coherent vector risk measure into a convex measure. We obtain a dual representation result that extends the characterization of coherent risk measures. In Chapter 2, we define a distribution-based vector risk measure and show that it coincides, under certain conditions, with a coherent risk measure. In the second part, we use stochastic control techniques to address two problems. Chapter 3 presents a characterization and a numerical solution of the value function for a consumption and investment optimization problem in a financial market with taxes on capital gains. Chapter 4 presents an explicit solution of the over-replication strategy of a contingent asset in the presence of partial transaction costs.