On extreme ruinous behaviour of Levy insurance risk processes

Reference:

Kluppelberg, C. and Kyprianou, A. E., 2006. On extreme ruinous behaviour of Levy insurance risk processes. Journal of Applied Probability, 43 (2), pp. 594-598.

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Official URL:

http://dx.doi.org/10.1239/jap/1152413744

Abstract

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 distribitions for a general class of Lévy insurance risk processes. The results bring the earlier conclusions of Asmussen and Klüppelberg (1996) for the Cramér-Lundberg process into greater generality.

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