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We study the asymptotics of the ruin probability in the Cram\'er-Lundbergmodel with a modified notion of ruin. The modification is as follows. If theportfolio becomes negative, the asset is not immediately declared ruined butmay survive due to certain mechanisms. Under a rather general assumption on themechanism - satisfied by most such modified models from the literature - westudy the relation of the asymptotics of the modified ruin probability to theclassical ruin probability. This is done under the Cram\'er condition as wellas for subexponential integrated claim sizes.

Ruin probabilities in the Cram\'er-Lundberg model with temporarily negative capital