De Finetti's optimal dividends problem with an affine penalty function at ruin

Ronnie L. Loeffen, Jean François Renaud

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    Abstract

    In 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. © 2009 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)98-108
    Number of pages10
    JournalInsurance: Mathematics and Economics
    Volume46
    Issue number1
    DOIs
    Publication statusPublished - Feb 2010

    Keywords

    • Deficit at ruin
    • Gerber-Shiu functions
    • Insurance risk theory
    • Lévy processes
    • Log-convexity
    • Optimal dividends
    • Stochastic control

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