Banks could achieve substantial improvements of their portfolio credit risk assessment by estimating rating transition matrices within a time-continuous Markov model, thereby using continuous-time rating transitions provided by internal rating systems instead of discrete-time rating information....

For a continuous-time Markov process, commonly, only discrete-time observations are available. We analyze multiple observations of a homogeneous Markov jump process with an absorbing state. We establish consistency of the maximum likelihood estimator, as the number of Markov processes increases....