Before revision:   As a reasonable trade-off between realistic stylized facts, practical demands, and mathematical tractability, we propose models leading to a Markovian multi-variate default-indicator process. The well-known "looping default" case is shown to be equipped with this property, to be linked to the classical "Freund distribution" , and to allow for a new construction with immediate multi-variate extensions.
After revision:  As a reasonable trade-off between realistic stylized facts, practical demands, and mathematical tractability, we propose models leading to a Markovian multi-variate survival--indicator process, and we investigate two instances of static models for the vector of default times from the statistical literature that fall into this class. On the one hand, the "looping default" case is shown to be equipped with this property, to be linked to the classical "Freund distribution" , and to allow for a new construction with immediate multi-variate extensions.