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Optimal joint survival reinsurance: An efficient frontier approach

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

Abstract

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
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    References listed on IDEAS

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    1. Gajek, Leslaw & Zagrodny, Dariusz, 2004. "Optimal reinsurance under general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 227-240, April.
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    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.
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    Citations

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    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, arXiv.org.
    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.

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