In this paper we study the connection between matrix measures and random walks with a tridiagonal block transition matrix. We derive sufficient conditions such that the blocks of the n-step transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued...

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....