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Asymptotic analysis of a risk process with high dividend barrier

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  • Frostig, Esther

Abstract

In this paper we study a risk model with constant high dividend barrier. We apply Keilson's (1966) results to the asymptotic distribution of the time until occurrence of a rare event in a regenerative process, and then results of the cycle maxima for random walk to obtain the asymptotic distribution of the time to ruin and the amount of dividends paid until ruin.

Suggested Citation

  • Frostig, Esther, 2010. "Asymptotic analysis of a risk process with high dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 21-26, August.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:1:p:21-26
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    References listed on IDEAS

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    1. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    2. 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, vol. 37(2), pages 324-334, October.
    3. Li, Shuanming & Garrido, Jose, 2004. "On a class of renewal risk models with a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 691-701, December.
    4. Frostig, Esther, 2005. "The expected time to ruin in a risk process with constant barrier via martingales," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 216-228, October.
    5. Dickson, David C.M. & Waters, Howard R., 2004. "Some Optimal Dividends Problems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 49-74, May.
    6. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    7. Gerber, Hans U. & Shiu, Elias S.W. & Smith, Nathaniel, 2006. "Maximizing Dividends without Bankruptcy," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 5-23, May.
    8. Hans Gerber & Elias Shiu, 2006. "On Optimal Dividend Strategies In The Compound Poisson Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 76-93.
    9. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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