Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Abstract

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

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Discrete Time Hybrid Semi-Markov Models in Manpower Planning

“…Furthermore, let T n and J n denote, respectively, the time of the n-th transition and the state occupied after the n-th transition. A semi-Markov process is equivalent to a Markov renewal process [37] and is completely determined by an initial distribution…”

Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

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