Albrecher, Hansjoerg and Constantinescu, Corina and Pirsic, Gottlieb and Regensburger, Georg and 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.
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| 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 |
|---|---|
| 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, |
| Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |
| Depositing User: | M.G. Rosenkranz |
| Date Deposited: | 30 May 2012 16:17 |
| Last Modified: | 08 Jun 2012 11:27 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/29601 (The current URI for this page, for reference purposes) |
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