Credit default prediction and parabolic potential theory

We consider an approach to credit risk in which the information about the time of bankruptcy is modelled using a Brownian bridge that starts at zero and is conditioned to equal zero when the default occurs. This raises the question whether the default can be foreseen by observing the evolution of the bridge process. Unlike in most standard models for credit risk, we allow the distribution of the default time to be singular. Using a well known fact from parabolic potential theory, we provide a sufficient condition for its predictability.