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Optimal Change-Loss Reinsurance Contract Design under Tail Risk Measures for Catastrophe Insurance

Author

Listed:
  • Nanjun ZHU

    (Peking University)

  • Yulin FENG

    (Tsinghua University)

Abstract

In this paper, the optimal reinsurance contract design problem for catastrophe insurance is studied using the general structure of reinsurance contracts, change-loss reinsurance. Closed-form solutions are derived under two tail risk measures, Value-at-Risk (VaR) and Conditional Tail Expectation (CTE). The results show that CTE is a robust risk measure in that the structure of the optimal reinsurance contract under CTE measure is always change-loss reinsurance. While the optimal reinsurance contract under VaR measure degenerates from change-loss reinsurance to quota-share reinsurance when the ceding company is less risk averse. The theoretical approach is also applied to earthquake insurance market in China’s Yunnan Province, and explicit solutions to the optimal reinsurance contract design problem under both VaR and CTE measures are obtained in the paper.

Suggested Citation

  • Nanjun ZHU & Yulin FENG, 2017. "Optimal Change-Loss Reinsurance Contract Design under Tail Risk Measures for Catastrophe Insurance," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(4), pages 225-242.
    • Handle: RePEc:cys:ecocyb:v:50:y:2017:i:4:p:225-242
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    References listed on IDEAS

    as
    1. Asimit, Alexandru V. & Chi, Yichun & Hu, Junlei, 2015. "Optimal non-life reinsurance under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 227-237.
    2. Kaluszka, Marek, 2001. "Optimal reinsurance under mean-variance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 61-67, February.
    3. Chi, Yichun & Lin, X. Sheldon, 2014. "Optimal Reinsurance With Limited Ceded Risk: A Stochastic Dominance Approach," ASTIN Bulletin, Cambridge University Press, vol. 44(1), pages 103-126, January.
    4. Kaluszka, Marek, 2005. "Optimal reinsurance under convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 375-398, June.
    5. Cheung, K.C. & Liu, F. & Yam, S.C.P., 2012. "Average Value-at-Risk Minimizing Reinsurance Under Wang's Premium Principle with Constraints," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 575-600, November.
    6. Carole Bernard & Weidong Tian, 2009. "Optimal Reinsurance Arrangements Under Tail Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 709-725, September.
    7. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    8. 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.
    9. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 93-112, May.
    10. Ken Seng Tan & Chengguo Weng, 2014. "Empirical Approach for Optimal Reinsurance Design," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(2), pages 315-342, April.
    11. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    12. Ken Seng Tan & Chengguo Weng, 2012. "Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 109-140, March.
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    More about this item

    Keywords

    Catastrophe Insurance; Change-Loss Reinsurance; Contract Design; Value-at-Risk; Conditional Tail Expectation.;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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