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Optimal reinsurance under risk and uncertainty

Author

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  • Balbás, Alejandro
  • Balbás, Beatriz
  • Balbás, Raquel
  • Heras, Antonio

Abstract

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the reinsurer moral hazard is totally eliminated.

Suggested Citation

  • Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel & Heras, Antonio, 2015. "Optimal reinsurance under risk and uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 61-74.
    • Handle: RePEc:eee:insuma:v:60:y:2015:i:c:p:61-74
    DOI: 10.1016/j.insmatheco.2014.11.001
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    References listed on IDEAS

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    Cited by:

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    2. Wael Hemrit, 2022. "Does insurance demand react to economic policy uncertainty and geopolitical risk? Evidence from Saudi Arabia," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(2), pages 460-492, April.
    3. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
    4. Birghila, Corina & Pflug, Georg Ch., 2019. "Optimal XL-insurance under Wasserstein-type ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 30-43.
    5. Hasan Dinçer & Serhat Yüksel & Seçil Şenel, 2018. "Analyzing the Global Risks for the Financial Crisis after the Great Depression Using Comparative Hybrid Hesitant Fuzzy Decision-Making Models: Policy Recommendations for Sustainable Economic Growth," Sustainability, MDPI, vol. 10(9), pages 1-15, September.
    6. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    7. Asimit, Vali & Boonen, Tim J., 2018. "Insurance with multiple insurers: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 778-790.
    8. Tim J. Boonen, 2016. "Optimal Reinsurance with Heterogeneous Reference Probabilities," Risks, MDPI, vol. 4(3), pages 1-11, July.
    9. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2018. "Golden options in financial mathematics," INDEM - Working Paper Business Economic Series 27672, Instituto para el Desarrollo Empresarial (INDEM).
    10. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2017. "Differential equations connecting VaR and CVaR," INDEM - Working Paper Business Economic Series 24017, Instituto para el Desarrollo Empresarial (INDEM).
    11. Kong, Dezhou & Liu, Lishan & Wu, Yonghong, 2018. "Optimal reinsurance under risk and uncertainty on Orlicz hearts," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 108-116.
    12. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel & Heras, Antonio, 2022. "Risk transference constraints in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 27-40.
    13. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.
    14. Massimiliano Amarante & Mario Ghossoub, 2016. "Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer," Risks, MDPI, vol. 4(1), pages 1-27, March.
    15. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2016. "Good deals and benchmarks in robust portfolio selection," European Journal of Operational Research, Elsevier, vol. 250(2), pages 666-678.
    16. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2016. "VaR as the CVaR sensitivity : applications in risk optimization," INDEM - Working Paper Business Economic Series id-16-01, Instituto para el Desarrollo Empresarial (INDEM).
    17. Hu, Duni & Chen, Shou & Wang, Hailong, 2018. "Robust reinsurance contracts with uncertainty about jump risk," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1175-1188.
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    More about this item

    Keywords

    Risk and uncertainty; Moral hazard; Optimal reinsurance and optimality conditions; Bang–bang solution; The optimal reinsurance linear problem;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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