Asymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases

Griffin, Philip SMaller, Rossvan Schaik, Kees2015-12-100167-6687http://hdl.handle.net/1885/65201Recent models of the insurance risk process use a Lévy process to generalise the traditional Cramér-Lundberg compound Poisson model. This paper is concerned with the behaviour of the distributions of the overshoot and undershoots of a high level, for aKeywords: Convolution equivalent distributions; Cramér condition; Insurance risk process; Lévy process; Overshoot; Ruin time; UndershootAsymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases201210.1016/j.insmatheco.2012.06.0052016-02-24