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

Albrecher, Hansjoerg, Constantinescu, Corina, Pirsic, Gottlieb, Regensburger, Georg, Rosenkranz, Markus (2010) An algebraic operator approach to the analysis of Gerber-Shiu functions. Insurance: Mathematics and Economics, 46 (1). pp. 42-51. ISSN 0167-6687. (doi:10.1016/j.insmatheco.2009.02.002) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:29601)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL: http://dx.doi.org/10.1016/j.insmatheco.2009.02.002

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.

Item Type:	Article
DOI/Identification number:	10.1016/j.insmatheco.2009.02.002
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders:	FWF Austrian Science Fund (https://ror.org/013tf3c58)
Depositing User:	Markus Rosenkranz
Date Deposited:	30 May 2012 16:17 UTC
Last Modified:	20 May 2025 11:35 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/29601 (The current URI for this page, for reference purposes)

University of Kent Author Information

Rosenkranz, Markus.

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