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Optimal reinsurance with general risk measures

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  • Balbás, Alejandro
  • Balbás, Beatriz
  • Heras, Antonio
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    Abstract

    This paper studies the optimal reinsurance problem when risk is measured by a general risk measure. Necessary and sufficient optimality conditions are given for a wide family of risk measures, including deviation measures, expectation bounded risk measures and coherent measures of risk. The optimality conditions are used to verify whether the classical reinsurance contracts (quota-share, stop-loss) are optimal essentially, regardless of the risk measure used. The paper ends by particularizing the findings, so as to study in detail two deviation measures and the conditional value at risk.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4V1TXKM-2/2/84b1e8c1a44c609c91a5897900bc5ba7
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 44 (2009)
    Issue (Month): 3 (June)
    Pages: 374-384

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    Handle: RePEc:eee:insuma:v:44:y:2009:i:3:p:374-384

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Optimal reinsurance Risk measure and deviation measure Optimality conditions;

    References

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    1. Laeven, Roger J. A. & Goovaerts, Marc J., 2004. "An optimization approach to the dynamic allocation of economic capital," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 299-319, October.
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    9. Kaluszka, Marek, 2001. "Optimal reinsurance under mean-variance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 61-67, February.
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    15. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    16. Gajek, Leslaw & Zagrodny, Dariusz, 2004. "Optimal reinsurance under general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 227-240, April.
    17. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    18. Kaluszka, Marek, 2005. "Optimal reinsurance under convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 375-398, June.
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    Citations

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    Cited by:
    1. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2010. "CAPM and APT-like models with risk measures," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1166-1174, June.
    2. Alejandro Balbas, 2008. "Capital requirements: Are they the best solution?," Business Economics Working Papers wb087114, Universidad Carlos III, Departamento de Economía de la Empresa.
    3. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 446-461.
    4. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    5. Cui, Wei & Yang, Jingping & Wu, Lan, 2013. "Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 74-85.
    6. Chi, Yichun, 2012. "Optimal reinsurance under variance related premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 310-321.
    7. Alejandro Balbas & Beatriz Balbas & Raquel Balbas, 2013. "Optimal Reinsurance: A Risk Sharing Approach," Risks, MDPI, Open Access Journal, vol. 1(2), pages 45-56, August.
    8. Alejandro Balbás & Raquel Balbás, 2009. "Compatibility between pricing rules and risk measures: The CCVaR," Business Economics Working Papers wb090201, Universidad Carlos III, Departamento de Economía de la Empresa.
    9. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
    10. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
    11. 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.
    12. Chi, Yichun & Weng, Chengguo, 2013. "Optimal reinsurance subject to Vajda condition," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 179-189.

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