PDE Approach to valuation and hedging of credit derivatives

Our aim is to examine the PDE approach to the valuation and hedging of a defaultable claim in various settings; this allows us to emphasize the importance of the choice of the traded assets. We start with a general model for the dynamics of the traded primary assets. Subsequently, we specify some particular models and we deal with particular defaultable claims such as, for instance, survival claims. In a first part, we examine the no-arbitrage property of a model in terms of a martingale measure. The following part is devoted to the study of the PDE approach to valuation of defaultable claims and we give the hedging strategies of a contingent claim under the assumption that prices of primary assets are strictly positive. Then, we study the particular case when one of the primary assets is a defaultable security with zero recovery, so that its price vanishes after default.