Intensity approach versus hazard process approach to modeling of credit risk

Work with T. Bielecki, Y. LeCam , M Rutkowski

We study the different models of credit risk and we present some cases where the hazard process approach is more efficient than the intensity approach. We compare the value of the intensity in different filtrations. We study the case of two correlated defaults in full generality, and we show how one can hedge first to default claims using CS.