De Finetti's optimal dividends problem with an affine penalty function at ruin
AbstractIn a Lévy insurance risk model, under the assumption that the tail of the Lévy measure is log-convex, we show that either a horizontal barrier strategy or the take-the-money-and-run strategy maximizes, among all admissible strategies, the dividend payments subject to an affine penalty function at ruin. As a key step for the proof, we prove that, under the aforementioned condition on the jump measure, the scale function of the spectrally negative Lévy process has a log-convex derivative.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 46 (2010)
Issue (Month): 1 (February)
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Web page: http://www.elsevier.com/locate/inca/505554
Insurance risk theory Optimal dividends Deficit at ruin Gerber-Shiu functions Levy processes Stochastic control Log-convexity;
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