ON SOME MEASURES OF THE SEVERITY OF RUIN IN THE CLASSICAL POISSON MODEL

In many circumstances the ruin of an insurance company is not definitive and this company can be rescued when its ruin is not too severe. This possibility of recovery depends on the state of the company at ruin time, but also on the claims this company could endure after that time, since these new claims could lead to an increase of the ruin severity and time spent with a negative surplus. To give a more precise meaning to this possibility of recovery, in addition to the severity and duration of ruin, we define two more complex indices: the maximal severity of ruin and the cost of recovery.