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 this paper, we consider a risk model which allows the insurer to partially reflect the recent claim experience in the determination of the next period’s premium rate. In a ruin context, similar mechanisms to the one proposed in this paper have been studied by, e.g., Tsai and Parker (2004),...