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Theory of Probability and Mathematical Statistics

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On excess-of-loss reinsurance

Authors: Hansjörg Albrecher and Jozef L. Teugels
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 7-22
MSC (2000): Primary 62P05, 62H20
Published electronically: December 30, 2009
MathSciNet review: 2494532
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Abstract: We discuss a unified framework to analyze the distribution of the number of claims and the aggregate claim sizes in an excess-of-loss reinsurance contract based upon the use of point processes and work out several examples explicitly. We first deal with a single excess-of-loss situation with an extra upper bound on the coverage of individual claims. Subsequently the results are extended to a reinsurance chain with $ k$ partners.

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Additional Information

Hansjörg Albrecher
Affiliation: Radon Institute, Austrian Academy of Sciences, Linz, Austria, and University of Linz, Altenbergerstrasse 69, A-4040 Linz, Austria

Jozef L. Teugels
Affiliation: EURANDOM, Technische Universiteit Eindhoven, The Netherlands, and Katholieke Universiteit Leuven, Leuven Center for Statistics, Celestijnenlaan 200B, B-3001 Heverlee, Belgium

Keywords: Reinsurance, point processes, thinning, Laplace--Stieltjes transform
Received by editor(s): August 20, 2008
Published electronically: December 30, 2009
Additional Notes: Supported by the Austrian Science Fund Project P18392
Article copyright: © Copyright 2009 American Mathematical Society