On extreme ruinous behaviour of Lévy insurance risk processes

In this short note we show how new fluctuation identities and their associated asymptotics, given in Vigon (2002), Klüppelberg et al. (2004) and Doney and Kyprianou (2006), provide the basis for establishing, in an elementary way, asymptotic overshoot and undershoot distributions for a general class of Levy insurance risk processes. The results bring the earlier conclusions of Asmussen and Klüppelberg (1996) for the Cramer-Lundberg process into greater generality.