IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

De Finetti's dividend problem and impulse control for a two-dimensional insurance risk process

  • Irmina Czarna
  • Zbigniew Palmowski
Registered author(s):

    Consider two insurance companies (or two branches of the same company) that receive premiums at different rates and then split the amount they pay in fixed proportions for each claim (for simplicity we assume that they are equal). We model the occurrence of claims according to a Poisson process. The ruin is achieved when the corresponding two-dimensional risk process first leaves the positive quadrant. We will consider two scenarios of the controlled process: refraction and impulse control. In the first case the dividends are payed out when the two-dimensional risk process exits the fixed region. In the second scenario, whenever the process hits the horizontal line, it is reduced by paying dividends to some fixed point in the positive quadrant where it waits for the next claim to arrive. In both models we calculate the discounted cumulative dividend payments until the ruin. This paper is the first attempt to understand the effect of dependencies of two portfolios on the joint optimal strategy of paying dividends. For example in case of proportional reinsurance one can observe the interesting phenomenon that choice of the optimal barrier depends on the initial reserves. This is in contrast with the one-dimensional Cram\'{e}r-Lundberg model where the optimal choice of the barrier is uniform for all initial reserves.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    File Function: Latest version
    Download Restriction: no

    Paper provided by in its series Papers with number 0906.2100.

    in new window

    Date of creation: Jun 2009
    Date of revision: Feb 2011
    Handle: RePEc:arx:papers:0906.2100
    Contact details of provider: Web page:

    References listed on IDEAS
    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.:

    as in new window
    1. De Vylder, F. & Goovaerts, M. J., 1988. "Recursive calculation of finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 1-7, January.
    2. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    3. Hu, Taizhong & Wu, Zhiqiang, 1999. "On dependence of risks and stop-loss premiums," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 323-332, May.
    4. De Vylder, F. Etienne & Goovaerts, Marc J., 1999. "Explicit finite-time and infinite-time ruin probabilities in the continuous case," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 155-172, May.
    5. Avram, Florin & Palmowski, Zbigniew & Pistorius, Martijn, 2008. "A two-dimensional ruin problem on the positive quadrant," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 227-234, February.
    6. Denuit, M. & Genest, C. & Marceau, E., 1999. "Stochastic bounds on sums of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 85-104, September.
    7. Dhaene, J. & Goovaerts, M. J., 1997. "On the dependency of risks in the individual life model," Insurance: Mathematics and Economics, Elsevier, vol. 19(3), pages 243-253, May.
    8. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
    9. Goovaerts, M. J. & Dhaene, J., 1996. "The compound Poisson approximation for a portfolio of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 81-85, May.
    10. Dhaene, Jan & Denuit, Michel, 1999. "The safest dependence structure among risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 11-21, September.
    11. Ambagaspitiya, Rohana S., 1999. "On the distributions of two classes of correlated aggregate claims," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 301-308, May.
    12. Chan, Wai-Sum & Yang, Hailiang & Zhang, Lianzeng, 2003. "Some results on ruin probabilities in a two-dimensional risk model," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 345-358, July.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:arx:papers:0906.2100. 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: (arXiv administrators)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.