IDEAS home Printed from
   My bibliography  Save this article

Optimal joint survival reinsurance: An efficient frontier approach


  • Dimitrova, Dimitrina S.
  • Kaishev, Vladimir K.


The problem of optimal excess of loss reinsurance with a limiting and a retention level is considered. It is demonstrated that this problem can be solved, combining specific risk and performance measures, under some relatively general assumptions for the risk model, under which the premium income is modelled by any non-negative, non-decreasing function, claim arrivals follow a Poisson process and claim amounts are modelled by any continuous joint distribution. As a performance measure, we define the expected profits at time x of the direct insurer and the reinsurer, given their joint survival up to x, and derive explicit expressions for their numerical evaluation. The probability of joint survival of the direct insurer and the reinsurer up to the finite time horizon x is employed as a risk measure. An efficient frontier type approach to setting the limiting and the retention levels, based on the probability of joint survival considered as a risk measure and on the expected profit given joint survival, considered as a performance measure is introduced. Several optimality problems are defined and their solutions are illustrated numerically on several examples of appropriate claim amount distributions, both for the case of dependent and independent claim severities.

Suggested Citation

  • Dimitrova, Dimitrina S. & Kaishev, Vladimir K., 2010. "Optimal joint survival reinsurance: An efficient frontier approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 27-35, August.
  • Handle: RePEc:eee:insuma:v:47:y:2010:i:1:p:27-35

    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. Gajek, Leslaw & Zagrodny, Dariusz, 2004. "Optimal reinsurance under general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 227-240, April.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Verlaak, Robert & Beirlant, Jan, 2003. "Optimal reinsurance programs: An optimal combination of several reinsurance protections on a heterogeneous insurance portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 381-403, October.
    4. Lesław Gajek & Dariusz Zagrodny, 2004. "Reinsurance Arrangements Maximizing Insurer's Survival Probability," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(3), pages 421-435.
    5. Guerra, Manuel & de Lourdes Centeno, Maria, 2008. "Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 529-539, April.
    6. Kaishev, Vladimir K. & Dimitrova, Dimitrina S., 2006. "Excess of loss reinsurance under joint survival optimality," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 376-389, December.
    7. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 374-384, June.
    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. Wenjun Jiang & Jiandong Ren & Ričardas Zitikis, 2017. "Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-22, February.
    2. repec:spr:mathme:v:85:y:2017:i:2:d:10.1007_s00186-017-0570-8 is not listed on IDEAS
    3. repec:eee:insuma:v:76:y:2017:i:c:p:48-55 is not listed on IDEAS
    4. Dutang, C. & Lefèvre, C. & Loisel, S., 2013. "On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 774-785.
    5. Castañer, A. & Claramunt, M.M. & Lefèvre, C., 2013. "Survival probabilities in bivariate risk models, with application to reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 632-642.
    6. Lefèvre, Claude & Picard, Philippe, 2011. "A new look at the homogeneous risk model," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 512-519.
    7. Başak Bulut Karageyik & Şule Şahin, 2016. "Optimal Retention Level for Infinite Time Horizons under MADM," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-24, December.
    8. Amir T. Payandeh-Najafabadi & Ali Panahi-Bazaz, 2017. "An Optimal Combination of Proportional and Stop-Loss Reinsurance Contracts From Insurer's and Reinsurer's Viewpoints," Papers 1701.05450,
    9. Anna Castañer & M.Mercè Claramunt & Maite Mármol, 2014. "Some optimization and decision problems in proportional reinsurance," UB Economics Working Papers 2014/310, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.


    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:insuma:v:47:y:2010:i:1:p:27-35. 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.