Optimization of asset portfolios subject to default risk.

Summary This thesis deals with the optimization of asset portfolios subject to default risk. The current crisis has allowed us to understand that it is important to take into account the risk of default to be able to give the real value of its portfolio. Indeed, due to the different exchanges of the financial market actors, the financial system has become a network of several connections which it is essential to identify in order to evaluate the risk of investing in a financial asset. In this thesis, we define a financial system with a finite number of connections and we propose a model of the dynamics of an asset in such a system by taking into account the connections between the different assets. The measurement of the correlation will be done through the jump intensity of the processes. Using Stochastic Differential Backward Equations (SDGE), we will derive the price of a contingent asset and take into account the model risk in order to better evaluate the optimal consumption and wealth if one invests in such a market.