An algebraic operator approach to the analysis of Gerber-Shiu functions

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serval:BIB_2A9D0367BB82
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
An algebraic operator approach to the analysis of Gerber-Shiu functions
Journal
Insurance: Mathematics & Economics
Author(s)
Albrecher H., Constantinescu C., Pirsic G., Regensburger G., Rosenkranz M.
ISSN
0167-6687
Publication state
Published
Issued date
2010
Peer-reviewed
Oui
Volume
46
Number
1
Pages
42-51
Language
english
Abstract
We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.
Web of science
Open Access
Yes
Create date
09/02/2009 18:39
Last modification date
20/08/2019 13:10
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