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Constant dividend barrier in a risk model with interclaim-dependent claim sizes

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  • Landriault, David
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    Abstract

    The risk model with interclaim-dependent claim sizes proposed by Boudreault et al. [Boudreault, M., Cossette, H., Landriault, D., Marceau, E., 2006. On a risk model with dependence between interclaim arrivals and claim sizes. Scand. Actur. J., 265-285] is studied in the presence of a constant dividend barrier. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber-Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Finally, we analyze the expected present value of dividend payments before ruin in the same class of risk models. An homogeneous integro-differential equation is derived and then solved. Its solution can be expressed as a different combination of the two fundamental solutions to the homogeneous integro-differential equation associated to the Gerber-Shiu discounted penalty function.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 1 (February)
    Pages: 31-38

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:31-38

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

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    1. Gerber, Hans U. & Shiu, Elias S. W., 1997. "The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 21(2), pages 129-137, November.
    2. Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 34(3), pages 391-408, June.
    3. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 29(3), pages 333-344, December.
    4. Li, Shuanming & Garrido, Jose, 2004. "On a class of renewal risk models with a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 35(3), pages 691-701, December.
    5. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 35(2), pages 245-254, October.
    6. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 37(2), pages 324-334, October.
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    Cited by:
    1. Cheung, Eric C.K., 2011. "A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 48(3), pages 384-397, May.
    2. Shi, Yafeng & Liu, Peng & Zhang, Chunsheng, 2013. "On the compound Poisson risk model with dependence and a threshold dividend strategy," Statistics & Probability Letters, Elsevier, Elsevier, vol. 83(9), pages 1998-2006.

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