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Methods for estimating the optimal dividend barrier and the probability of ruin

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  • Gerber, Hans U.
  • Shiu, Elias S.W.
  • Smith, Nathaniel

Abstract

In applications of collective risk theory, complete information about the individual claim amount distribution is often not known, but reliable estimates of its first few moments may be available. For such a situation, this paper develops methods for estimating the optimal dividend barrier and the probability of ruin. In particular, two De Vylder approximations are explained, and the first and second order diffusion approximations are examined. For several claim amount distributions, the approximate values are compared numerically with the exact values. The De Vylder and diffusion approximations can be adapted to the more general situation where the aggregate claims process is a Lévy process with nonnegative increments.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:243-254
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    References listed on IDEAS

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    1. Dufresne, François & Gerber, Hans U. & Shiu, Elias S. W., 1991. "Risk Theory with the Gamma Process," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 21(02), pages 177-192, November.
    2. Chan, Beda, 1990. "Ruin Probability for Translated Combination of Exponential Claims," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 20(01), pages 113-114, April.
    3. Dickson, D. C. M. & Drekic, S., 2006. "Optimal Dividends Under a Ruin Probability Constraint," Annals of Actuarial Science, Cambridge University Press, vol. 1(02), pages 291-306, September.
    4. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400, September.
    5. Gerber, Hans U. & Lin, X. Sheldon & Yang, Hailiang, 2006. "A Note on the Dividends-Penalty Identity and the Optimal Dividend Barrier," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(02), pages 489-503, November.
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    Citations

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    Cited by:

    1. Liu, Zaiming & Li, Manman & Ameer, Sherbaz, 2009. "Methods for estimating optimal Dickson and Waters modification dividend barrier," Economic Modelling, Elsevier, vol. 26(5), pages 886-892, September.
    2. Yuen, Kam-Chuen & Zhou, Ming & Guo, Junyi, 2008. "On a risk model with debit interest and dividend payments," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2426-2432, October.
    3. repec:eee:insuma:v:76:y:2017:i:c:p:48-55 is not listed on IDEAS
    4. Wang, Chunwei & Yin, Chuancun & Li, Erqiang, 2010. "On the classical risk model with credit and debit interests under absolute ruin," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 427-436, March.
    5. 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.

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