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Optimal dividends with incomplete information in the dual model


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  • Gerber, Hans U.
  • Smith, Nathaniel
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    In [Gerber, H.U., Shiu, E.S.W., Smith, N., 2008. Methods for estimating the optimal dividend barrier and the probability of ruin. Insurance: Math. Econ. 42 (1), 243-254], methods were analyzed for estimating the optimal dividend barrier (in the sense of de Finetti). In particular, De Vylder approximations and diffusion approximations are discussed. These methods are useful when only the first few moments of the claim amount distribution are known. The purpose of this paper is to examine these and other methods (such as the gamma approximations and the gamproc approximations) in the dual model, see [Avanzi, B., Gerber, H.U., Shiu, E.S., 2007. Optimal dividends in the dual model. Insurance: Math. Econ. 41 (1), 111-123]. The dual model is obtained if the roles of premiums and claims are exchanged. In other words, the company has random gains, which constitute a compound Poisson process, and expenses occur continuously at a constant rate. The approximations can easily be implemented, and their accuracy is surprisingly good. Several numerical illustrations enhance the paper.

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    Bibliographic Info

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

    Volume (Year): 43 (2008)
    Issue (Month): 2 (October)
    Pages: 227-233

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    Handle: RePEc:eee:insuma:v:43:y:2008:i:2:p:227-233

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    Keywords: Optimal dividend barrier De Vylder approximations Diffusion approximations Gamma approximations Gamma process approximations;


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    1. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
    2. Gerber, Hans U. & Shiu, Elias S.W. & Smith, Nathaniel, 2008. "Methods for estimating the optimal dividend barrier and the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 243-254, February.
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    Cited by:
    1. Hongshuai Dai & Zaiming Liu & Nana Luan, 2010. "Optimal dividend strategies in a dual model with capital injections," Computational Statistics, Springer, vol. 72(1), pages 129-143, August.
    2. Avanzi, Benjamin & Cheung, Eric C.K. & Wong, Bernard & Woo, Jae-Kyung, 2013. "On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 98-113.
    3. Afonso, Lourdes B. & Cardoso, Rui M.R. & EgĂ­dio dos Reis, Alfredo D., 2013. "Dividend problems in the dual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 906-918.
    4. Ng, Andrew C.Y., 2009. "On a dual model with a dividend threshold," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 315-324, April.
    5. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.


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