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Optimal dividends with incomplete information in the dual model

Author

Listed:
  • Gerber, Hans U.
  • Smith, Nathaniel

Abstract

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.

Suggested Citation

  • Gerber, Hans U. & Smith, Nathaniel, 2008. "Optimal dividends with incomplete information in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 227-233, October.
  • Handle: RePEc:eee:insuma:v:43:y:2008:i:2:p:227-233
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    References listed on IDEAS

    as
    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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    Citations

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    Cited by:

    1. Cheung, Eric C.K. & Wong, Jeff T.Y., 2017. "On the dual risk model with Parisian implementation delays in dividend payments," European Journal of Operational Research, Elsevier, vol. 257(1), pages 159-173.
    2. Afonso, Lourdes B. & Cardoso, Rui M.R. & Egídio dos Reis, Alfredo D., 2013. "Dividend problems in the dual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 906-918.
    3. repec:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0755-3 is not listed on IDEAS
    4. repec:eee:insuma:v:76:y:2017:i:c:p:48-55 is not listed on IDEAS
    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.
    6. repec:eee:insuma:v:77:y:2017:i:c:p:1-13 is not listed on IDEAS
    7. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums," Papers 1604.06892, arXiv.org.
    8. Hu, Xiang & Yang, Hailiang & Zhang, Lianzeng, 2015. "Optimal retention for a stop-loss reinsurance with incomplete information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 15-21.
    9. repec:spr:compst:v:72:y:2010:i:1:p:129-143 is not listed on IDEAS
    10. repec:spr:joptap:v:167:y:2015:i:1:d:10.1007_s10957-014-0653-0 is not listed on IDEAS
    11. 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.
    12. 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.
    13. repec:eee:insuma:v:74:y:2017:i:c:p:135-146 is not listed on IDEAS
    14. Hongshuai Dai & Zaiming Liu & Nana Luan, 2010. "Optimal dividend strategies in a dual model with capital injections," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(1), pages 129-143, August.
    15. repec:spr:joptap:v::y::i::d:10.1007_s10957-016-1050-7 is not listed on IDEAS
    16. Jos'e-Luis P'erez & Kazutoshi Yamazaki, 2016. "Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities," Papers 1612.02444, arXiv.org, revised Jan 2018.
    17. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums," Papers 1605.04584, arXiv.org.
    18. Chen, Shumin & Wang, Xi & Deng, Yinglu & Zeng, Yan, 2016. "Optimal dividend-financing strategies in a dual risk model with time-inconsistent preferences," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 27-37.
    19. Chuancun Yin & Kam Chuen Yuen, 2014. "Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs," Papers 1409.0407, arXiv.org.

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