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An optimal dividends problem with transaction costs for spectrally negative Lévy processes

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  • Loeffen, R.L.

Abstract

We consider an optimal dividends problem with transaction costs where the reserves are modeled by a spectrally negative Lévy process. We make the connection with the classical de Finetti problem and show in particular that when the Lévy measure has a log-convex density, then an optimal strategy is given by paying out a dividend in such a way that the reserves are reduced to a certain level c1 whenever they are above another level c2. Further we describe a method to numerically find the optimal values of c1 and c2.

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  • 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.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:41-48
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    1. Dufresne, François & Gerber, Hans U. & Shiu, Elias S. W., 1991. "Risk Theory with the Gamma Process," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 177-192, November.
    2. Luis H. R. Alvarez & Teppo A. Rakkolainen, 2007. "Optimal Dividend Control in Presence of Downside Risk," Discussion Papers 14, Aboa Centre for Economics.
    3. 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.
    4. Dufresne, F. & Gerber, H. U., 1993. "The probability of ruin for the Inverse Gaussian and related processes," Insurance: Mathematics and Economics, Elsevier, vol. 12(1), pages 9-22, February.
    5. A. Kyprianou & B. Surya, 2007. "Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels," Finance and Stochastics, Springer, vol. 11(1), pages 131-152, January.
    6. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 27-58, March.
    7. Agnès Sulem, 1986. "A Solvable One-Dimensional Model of a Diffusion Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 125-133, February.
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