BEN TAHAR Imen

The back cover states: "This book is an introduction to stochastic calculus motivated by applications in finance and insurance. It contains six chapters. The first one is an introduction to the finance concepts that will be used later: no arbitrage opportunity, risk-neutral probability, replication, complete market, etc. It is followed by an introduction to stochastic calculus accessible to first year master students. We present Brownian motion, the stochastic integral and the rudiments of stochastic calculus(.).

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.