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...

A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically from finance, especially for path-dependent option...