# Dividend problem with Parisian delay for a spectrally negative L\'evy risk process

## Author Info

• Irmina Czarna
• Zbigniew Palmowski
Registered author(s):

## Abstract

In this paper we consider dividend problem for an insurance company whose risk evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments) when Parisian delay is applied. The objective function is given by the cumulative discounted dividends received until the moment of ruin when so-called barrier strategy is applied. Additionally we will consider two possibilities of delay. In the first scenario ruin happens when the surplus process stays below zero longer than fixed amount of time $\zeta>0$. In the second case there is a time lag $d$ between decision of paying dividends and its implementation.

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File URL: http://arxiv.org/pdf/1004.3310

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1004.3310.

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 Length: Date of creation: Apr 2010 Date of revision: Oct 2011 Handle: RePEc:arx:papers:1004.3310 Contact details of provider: Web page: http://arxiv.org/

## References

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1. Irmina Czarna & Zbigniew Palmowski, 2010. "Ruin probability with Parisian delay for a spectrally negative L\'evy risk process," Papers 1003.4299, arXiv.org, revised Apr 2010.
2. 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.
3. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
4. 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.
5. 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.
6. Marc Hallin, 1978. "Band strategies: the random walk of reserves," ULB Institutional Repository 2013/1989, ULB -- Universite Libre de Bruxelles.
7. Dickson, David C.M. & Waters, Howard R., 2004. "Some Optimal Dividends Problems," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 34(01), pages 49-74, May.
8. Albrecher, Hansjörg & Thonhauser, Stefan, 2008. "Optimal dividend strategies for a risk process under force of interest," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 134-149, August.
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