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

By Hansjoerg Albrecher, Corina Constantinescu, Gottlieb Pirsic, Georg Regensburger and Markus Rosenkranz


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.\u

Topics: QA150, QA273, QA372, QA76
Publisher: Academic Press Ltd Elsevier Science Ltd
Year: 2010
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