Chen, Jinyuan; Kong, Xinbing; Li, Zehui The Gerber-Shiu function for a risk model perturbed by stable Lévy motion. (Chinese. English summary) Zbl 1265.60092 Acta Math. Sin., Chin. Ser. 55, No. 2, 259-272 (2012). Summary: Following a weak convergence approach, the present paper for the first time gives a representation of the Gerber-Shiu expected discounted penalty function (the G-S function) of a risk process perturbed by an \(\alpha\)-stable Lévy motion in terms of the Laplace transform. Using the same method, this paper also gives the ultimate ruin probability. We find that the ultimate ruin probability of the risk process is indeed a special case of the G-S function. MSC: 60G52 Stable stochastic processes 60F15 Strong limit theorems 91B30 Risk theory, insurance (MSC2010) Keywords:compound Poisson process; \(\alpha\)-stable Lévy motion; ruin probability; Gerber-Shiu expected discounted penalty function; Skorohod topology PDFBibTeX XMLCite \textit{J. Chen} et al., Acta Math. Sin., Chin. Ser. 55, No. 2, 259--272 (2012; Zbl 1265.60092)