Inspired by Parisian barrier options in finance (see e.g. Chesney et al. (1997)), a new definition of the event "ruin" for an insurance risk model is considered. As in Dassios and Wu (2009), the surplus process is allowed to spend time under a pre-specified default level before ruin is...

In ruin theory, an insurer’s income process is usually assumed to grow at a deterministic rate of c 0 over time. For instance, both the well-known Cramér-Lundberg risk process and the Sparre Andersen risk model have this assumption built in the construction of their respective surplus...