On the Gerber-Shiu function and change of measure
We consider several models for the surplus of an insurance company mainly under some light-tail assumptions. We are interested in the expected discounted penalty at ruin. By a change of measure we remove the discounting, which simplifies the expression. This leads to (defective) renewal equations as they had been found by different methods in the literature. If we use the change of measure such that ruin becomes certain, the renewal equations simplify to ordinary renewal equations. This helps to discuss the asymptotics as the initial capital goes to infinity. For phase-type claim sizes, explicit formulae can be derived.
Year of publication: |
2010
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Authors: | Schmidli, Hanspeter |
Published in: |
Insurance: Mathematics and Economics. - Elsevier, ISSN 0167-6687. - Vol. 46.2010, 1, p. 3-11
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Publisher: |
Elsevier |
Keywords: | Expected discounted penalty function Change of measure Laplace transform Sparre-Andersen risk model Markov-modulated risk model Bjork-Grandell risk model Perturbed risk model Lump sum premia |
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