10. Advanced Bankruptcy Concepts

So far we focused on the event of ruin, corresponding to the reserve process dropping below 0. This chapter studies various bankruptcy concepts, in which, besides the reserve level becoming negative, an additional condition has to be fulfilled. In the first variant, the net reserve process is inspected at Poisson instants, and bankruptcy occurs if the reserve level is below zero at such an inspection time. For this setting an adapted version of the Pollaczek-Khinchine theorem is derived, as well as an appealing decomposition. In the second variant there is bankruptcy if the reserve process is uninterruptedly below 0 for a sufficiently long time, whereas in the third variant the bankruptcy criterion is based on the total time with a negative surplus.