Automatic Synthesis of Tri-Diagonal Markov Transition Matrices: A Failure of the Inverse Ferron-Frobenius Algorithm


Sylvain Raynes experimented with a method developed by Goya and Boyarski (1993) to standardize the synthesis of conditional Markov transition matrices for deal entry in our automated re-rating system, ABSTRAK®. In the analytical literature, the reverse-engineering of a Markov matrix from its spectral-radius eigenvector is referred to as the Inverse Perron-Frobenius Problem. Our analysts do this synthesis manually, so a successful outcome based on a numerical method would add considerable efficiency and precision to our process. Unfortunately, the method produced forward roll-rates too small for real-world delinquency modeling.

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