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

  • Loeffen, Ronnie L.
  • Renaud, Jean-François
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4X9TTPJ-1/2/552b276eb00549a552c4c8ba58b9cb2f
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 1 (February)
    Pages: 98-108

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    Handle: RePEc:eee:insuma:v:46:y:2010:i:1:p:98-108
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
    2. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    3. An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers 95-03, Duke University, Department of Economics.
    4. repec:spr:compst:v:69:y:2009:i:1:p:27-58 is not listed on IDEAS
    5. Luis H. R. Alvarez & Teppo A. Rakkolainen, 2007. "Optimal Dividend Control in Presence of Downside Risk," Discussion Papers 14, Aboa Centre for Economics.
    6. Kulenko, Natalie & Schmidli, Hanspeter, 2008. "Optimal dividend strategies in a Cramér-Lundberg model with capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 270-278, October.
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