An algebraic operator approach to the analysis of Gerber-Shiu functions |
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Authors: | Hansjörg Albrecher Corina Constantinescu |
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Institution: | a Institute of Actuarial Science, Faculty HEC, University of Lausanne, Extranef Building, CH-1015 Lausanne, Switzerland b Johann Radon Institute for Computational and Applied Mathematics (RICAM), Altenbergerstrasse 69, A-4040 Linz, Austria |
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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. |
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