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On a multivariate Markov chain model for credit risk measurement. (English) Zbl 1134.91485
Summary: We use credibility theory to estimate credit transition matrices in a multivariate Markov chain model for credit rating. A transition matrix is estimated by a linear combination of the prior estimate of the transition matrix and the empirical transition matrix. These estimates can be easily computed by solving a set of linear programming (LP) problems. The estimation procedure can be implemented easily on Excel spreadsheets without requiring much computational effort and time. The number of parameters is $O(s^{2}m^{2})$, where $s$ is the dimension of the categorical time series for credit ratings and $m$ is the number of possible credit ratings for a security. Numerical evaluations of credit risk measures based on our model are presented.

91B30Risk theory, insurance
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