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The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function

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  • Sheldon Lin, X.
  • E. Willmot, Gordon
  • Drekic, Steve
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    Bibliographic Info

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

    Volume (Year): 33 (2003)
    Issue (Month): 3 (December)
    Pages: 551-566

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    Handle: RePEc:eee:insuma:v:33:y:2003:i:3:p:551-566

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

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Dickson, David C. M. & Hipp, Christian, 1998. "Ruin probabilities for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 22(3), pages 251-262, July.
    2. 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.
    3. Cai, Jun & Dickson, David C. M., 2002. "On the expected discounted penalty function at ruin of a surplus process with interest," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 30(3), pages 389-404, June.
    4. Willmot, Gordon E. & Dickson, David C. M., 2003. "The Gerber-Shiu discounted penalty function in the stationary renewal risk model," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 32(3), pages 403-411, July.
    5. 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.
    6. Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 16(1), pages 7-22, April.
    7. Paulsen, Jostein & Gjessing, Hakon K., 1997. "Optimal choice of dividend barriers for a risk process with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 20(3), pages 215-223, October.
    8. Dufresne, Francois & Gerber, Hans U., 1988. "The probability and severity of ruin for combinations of exponential claim amount distributions and their translations," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 7(2), pages 75-80, April.
    9. Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 25(1), pages 63-84, September.
    10. Lin, X. Sheldon & Willmot, Gordon E., 2000. "The moments of the time of ruin, the surplus before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 27(1), pages 19-44, August.
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    Cited by:
    1. Yang, Wenquan & Hu, Yijun, 2009. "Upper bounds for ultimate ruin probabilities in the Sparre Andersen risk model with interest and a nonlinear dividend barrier," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(1), pages 63-69, January.
    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.
    3. Bo, Lijun & Song, Renming & Tang, Dan & Wang, Yongjin & Yang, Xuewei, 2012. "Lévy risk model with two-sided jumps and a barrier dividend strategy," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 50(2), pages 280-291.
    4. Li, Shuanming & Lu, Yi, 2009. "The distribution of total dividend payments in a Sparre Andersen model," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(9), pages 1246-1251, May.
    5. Yuen, Kam-Chuen & Zhou, Ming & Guo, Junyi, 2008. "On a risk model with debit interest and dividend payments," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(15), pages 2426-2432, October.
    6. Frostig, Esther, 2005. "The expected time to ruin in a risk process with constant barrier via martingales," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 37(2), pages 216-228, October.
    7. Peng, Dan & Liu, Donghai & Liu, Zaiming, 2013. "Dividend problems in the dual risk model with exponentially distributed observation time," Statistics & Probability Letters, Elsevier, Elsevier, vol. 83(3), pages 841-849.
    8. Kim, Bara & Kim, Hwa-Sung & Kim, Jeongsim, 2008. "A risk model with paying dividends and random environment," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(2), pages 717-726, April.
    9. Zhang, H.Y. & Zhou, M. & Guo, J.Y., 2006. "The Gerber-Shiu discounted penalty function for classical risk model with a two-step premium rate," Statistics & Probability Letters, Elsevier, Elsevier, vol. 76(12), pages 1211-1218, July.
    10. Yuan, Haili & Hu, Yijun, 2008. "Absolute ruin in the compound Poisson risk model with constant dividend barrier," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(14), pages 2086-2094, October.
    11. Frostig, Esther, 2010. "Asymptotic analysis of a risk process with high dividend barrier," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(1), pages 21-26, August.
    12. Yang, Hu & Zhang, Zhimin, 2009. "The perturbed compound Poisson risk model with multi-layer dividend strategy," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(1), pages 70-78, January.
    13. Feng, Runhuan, 2009. "On the total operating costs up to default in a renewal risk model," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 45(2), pages 305-314, October.
    14. Yang, Hu & Zhang, Zhimin & Lan, Chunmei, 2008. "On the time value of absolute ruin for a multi-layer compound Poisson model under interest force," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(13), pages 1835-1845, September.
    15. Geng, Xianmin & Wang, Ying, 2012. "The compound Pascal model with dividends paid under random interest," Statistics & Probability Letters, Elsevier, Elsevier, vol. 82(7), pages 1331-1336.
    16. Chen, Xu & Xiao, Ting & Yang, Xiang-qun, 2014. "A Markov-modulated jump-diffusion risk model with randomized observation periods and threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 54(C), pages 76-83.
    17. Willmot, Gordon E., 2004. "A note on a class of delayed renewal risk processes," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 34(2), pages 251-257, April.

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