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Limit distributions for risk processes in case of claim amounts of finite expectation

Authors:	K Jansen J Haezendonck F Delbaen

Institution:	Universiteit Antwerpen, U.I.A., Department Wiskunde, Universiteitsplein 1, B-2610 Wilrijk, Belgium;Universiteit Antwerpen, U.I.A., Department Wiskunde, Universiteitsplein 1, B-2610 Wilrijk, Belgium;Vrije Universiteit Brussel, Departement Wiskunde, Pleinlaan 2, B-1050 Brussel, Belgium

Abstract:	We prove limit theorems for the distribution of $Z_{l} if {Z_{l} :l ? R_{+}}$ is a risk process with claim amounts of finite mean. The results are illustrated by several examples and counterexamples.

Keywords:	Counting process Risk process Limiting distributions Lindeberg condition Central limit theorem Stable distribution Lévy function Lévy representation of an infinitely divisible distribution Domain of normal attraction
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