IDEAS home Printed from
   My bibliography  Save this article

On a risk model with debit interest and dividend payments


  • Yuen, Kam-Chuen
  • Zhou, Ming
  • Guo, Junyi


We consider the compound Poisson risk model with debit interest and dividend payments. The model assumes that the company is allowed to borrow at some debit interest rate when the surplus turns negative, and that the premium incomes are paid out as dividends to shareholders when the surplus reaches a horizontal barrier of level b. We first derive integro-differential equations for the expected discounted value of all dividends until absolute ruin, Vb(u), which is twice continuously differentiable. In the case of exponential claim amounts, we obtain explicit expressions for Vb(u) and the optimal barrier b* which maximizes Vb(u). We then perform a similar study for the Gerber-Shiu expected discounted penalty function. Again, when claims are exponentially distributed, we are able to find explicit expressions for the joint distribution of the surplus just prior to absolute ruin and the deficit at absolute ruin, which is a special case of the Gerber-Shiu function.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2426-2432

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Zhang, Chunsheng & Wu, Rong, 1999. "On the distribution of the surplus of the D-E model prior to and at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 309-321, May.
    2. 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, vol. 20(3), pages 215-223, October.
    3. 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.
    4. 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.
    5. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
    6. 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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Yin, Chuancun & Yuen, Kam Chuen, 2011. "Optimality of the threshold dividend strategy for the compound Poisson model," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1841-1846.
    2. Zhou, Ming & Yuen, Kam C., 2012. "Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle," Economic Modelling, Elsevier, vol. 29(2), pages 198-207.
    3. Li, Manman & Liu, Zaiming, 2012. "Regulated absolute ruin problem with interest structure and linear dividend barrier," Economic Modelling, Elsevier, vol. 29(5), pages 1786-1792.
    4. Zhang, Yuanyuan & Wang, Wensheng, 2012. "Ruin probabilities of a bidimensional risk model with investment," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 130-138.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2426-2432. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.