Some Markov Chains have very useful characteristics. Especially in the case of credit risk, we are interested in concepts such as the probability of default, the passing of time between an initial state and default and topics such as the setting where we have more than one Markov-driven economic agent and where the credit status of one may affect the others.

We will see that for such special cases with a transition matrix that satisfies some well defined conditions, it is possible to compute the aluded probabilities with just a few matrix operations. In this Maple document we use examples to illustrate the application of the most commonly used theorems of Markov Chains. Topics include:

• Absorbing Markov Chains
• Ergodic and Regular Markov Chains
• Some Useful Theorems for Ergodic and Regular Chains
• Mean First Passage Time for Ergodic Chains
• Stepping Stone Model
• Credit Risk Term Structure and the Implicit Markov Process

This is part 34 of a 45-document course on Modeling Financial Markets.