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Obtaining the dividends-penalty identities by interpretation

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  • Gerber, Hans U.
  • Yang, Hailiang

Abstract

The dividends-penalty identity is a relation between three functions: the discounted penalty function without dividends, the discounted penalty function if a barrier dividend strategy is applied, and the expected discounted dividends until ruin. The classical model of risk theory is modified in that the deterministic premiums are replaced by a compound Poisson process with exponential jumps. In this model, the dividends-penalty identity is new and can be derived by interpretation. Then the dividends-penalty identity in the classical model is obtained as a limit.

Suggested Citation

  • Gerber, Hans U. & Yang, Hailiang, 2010. "Obtaining the dividends-penalty identities by interpretation," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 206-207, October.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:2:p:206-207
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    References listed on IDEAS

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    1. Yuen, Kam C. & Wang, Guojing & Li, Wai K., 2007. "The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 104-112, January.
    2. Hansjörg Albrecher & Hans Gerber & Hailiang Yang, 2010. "A Direct Approach to the Discounted Penalty Function," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(4), pages 420-434.
    3. 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.
    4. Gerber, Hans U. & Lin, X. Sheldon & Yang, Hailiang, 2006. "A Note on the Dividends-Penalty Identity and the Optimal Dividend Barrier," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 489-503, November.
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    Cited by:

    1. 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, vol. 50(2), pages 280-291.
    2. Xie, Jiayi & Zhang, Zhimin, 2020. "Statistical estimation for some dividend problems under the compound Poisson risk model," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 101-115.

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