This book will present transitions of credit risks among the ratings using semi-Markov models in view to solve the problems of duration, business cycle and the dependence not only on the last rating but also on the previous ratings and the aging. In this manner we present for the first time a more general version than the classical approach with Markov processes.
The first problem can be solved by means of semi-Markov environment in which the transition probability among the ratings is function of the duration, the second problem by means of the introduction of the non-homogeneity. Concerning the third problem named in literature named “the downward problem” i.e. the arrival to a state from a higher rating will imply a higher probability to go in the next transition to lower ratings.
The third problem in literature is named “the downward problem” i.e. the arrival to a state from a higher rating will imply a higher probability to go in the next transition to lower ratings.
Finally, the aging inside the rating will be faced by the introduction of recurrence time and an indexed model with the age as index. The models we construct will be applied to the financial management of insurance companies but there are also valid for banks.
