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Optimal Dividends Paid in a Foreign Currency for a L\'evy Insurance Risk Model

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  • Julia Eisenberg
  • Zbigniew Palmowski

Abstract

This paper considers an optimal dividend distribution problem for an insurance company where the dividends are paid in a foreign currency. In the absence of dividend payments, our risk process follows a spectrally negative L\'evy process. We assume that the exchange rate is described by a an exponentially L\'evy process, possibly containing the same risk sources like the surplus of the insurance company under consideration. The control mechanism chooses the amount of dividend payments. The objective is to maximise the expected dividend payments received until the time of ruin and a penalty payment at the time of ruin, which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. Via the corresponding Hamilton--Jacobi--Bellman equation we find the necessary and sufficient conditions for optimality of a single dividend barrier strategy. A number of numerical examples illustrate the theoretical analysis.

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  • Julia Eisenberg & Zbigniew Palmowski, 2020. "Optimal Dividends Paid in a Foreign Currency for a L\'evy Insurance Risk Model," Papers 2001.03733, arXiv.org.
    • Handle: RePEc:arx:papers:2001.03733
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    References listed on IDEAS

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    1. Nicole Bäuerle & Anja Blatter & Alfred Müller, 2008. "Dependence properties and comparison results for Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 161-186, February.
    2. Eisenberg, Julia, 2015. "Optimal dividends under a stochastic interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 259-266.
    3. Akyildirim, Erdinç & Güney, I. Ethem & Rochet, Jean-Charles & Soner, H. Mete, 2014. "Optimal dividend policy with random interest rates," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 93-101.
    4. Pablo Azcue & Nora Muler, 2005. "Optimal Reinsurance And Dividend Distribution Policies In The Cramér‐Lundberg Model," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 261-308, April.
    5. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    6. Kim Christensen & Roel Oomen & Roberto Renò, 2018. "The drift burst hypothesis," CREATES Research Papers 2018-21, Department of Economics and Business Economics, Aarhus University.
    7. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, vol. 4(3), pages 299-324.
    8. 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.
    9. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
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