Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and...

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...