Abstract
Inspired by Parisian barrier options in finance (see e.g. Chesney et al. (1997)), a new definition of the event 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 recognized. In this paper, we capitalize on the idea of Erlangian horizons (see Asmussen et al. (2002) and Kyprianou and Pistorius (2003)) and, thus assume an implementation delay of a mixed Erlang nature. Using the modern language of scale functions, we study the Laplace transform of this Parisian time to default in an insurance risk model driven by a spectrally negative Levy process of bounded variation. In the process, a generalization of the two-sided exit problem for this class of processes is further obtained.
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