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2010
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info:eu-repo/semantics/altIdentifier/doi/10.1016/j.insmatheco.2009.02.002
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info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:serval-BIB_2A9D0367BB827
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H. Albrecher et al., « An algebraic operator approach to the analysis of Gerber-Shiu functions », Serveur académique Lausannois, ID : 10.1016/j.insmatheco.2009.02.002
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Résumé
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.