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

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

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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/inca/505554

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    Keywords: Insurance risk theory Optimal dividends Deficit at ruin Gerber-Shiu functions Levy processes Stochastic control Log-convexity;

    References

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    1. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, Elsevier, vol. 80(2), pages 350-369, June.
    2. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 45(1), pages 41-48, August.
    3. Kulenko, Natalie & Schmidli, Hanspeter, 2008. "Optimal dividend strategies in a Cramér-Lundberg model with capital injections," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 43(2), pages 270-278, October.
    4. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 41(1), pages 163-184, July.
    5. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Computational Statistics, Springer, Springer, vol. 69(1), pages 27-58, March.
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    Cited by:
    1. Masahiko Egami & Kazutoshi Yamazaki, 2010. "Solving Optimal Dividend Problems via Phase-Type Fitting Approximation of Scale Functions," Discussion papers, Graduate School of Economics Project Center, Kyoto University e-10-011, Graduate School of Economics Project Center, Kyoto University.
    2. Yin, Chuancun & Wen, Yuzhen, 2013. "Optimal dividend problem with a terminal value for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 53(3), pages 769-773.
    3. Bo, Lijun & Song, Renming & Tang, Dan & Wang, Yongjin & Yang, Xuewei, 2012. "Lévy risk model with two-sided jumps and a barrier dividend strategy," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 50(2), pages 280-291.
    4. Yao, Dingjun & Yang, Hailiang & Wang, Rongming, 2014. "Optimal risk and dividend control problem with fixed costs and salvage value: Variance premium principle," Economic Modelling, Elsevier, Elsevier, vol. 37(C), pages 53-64.
    5. Liang, Zhibin & Young, Virginia R., 2012. "Dividends and reinsurance under a penalty for ruin," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 50(3), pages 437-445.

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