An optimal dividends problem with a terminal value for spectrally negative Lévy processes with a completely monotone jump density

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    Abstract

    We consider a modified version of the classical optimal dividends problem of de Finetti in which the objective function is altered by adding in an extra term which takes account of the ruin time of the risk process, the latter being modeled by a spectrally negative Lévy process. We show that, with the exception of a small class, a barrier strategy forms an optimal strategy under the condition that the Lévy measure has a completely monotone density. As a prerequisite for the proof, we show that, under the aforementioned condition on the Lévy measure, the q-scale function of the spectrally negative Lévy process has a derivative which is strictly log-convex. © Applied Probability Trust 2009.
    Original languageEnglish
    Pages (from-to)85-98
    Number of pages13
    JournalJournal of Applied Probability
    Volume46
    Issue number1
    DOIs
    Publication statusPublished - Mar 2009

    Keywords

    • Complete monotonicity
    • Dividend problem
    • Lévy process
    • Scale function
    • Stochastic control

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