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Optimal reinsurance subject to Vajda condition

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  • Chi, Yichun
  • Weng, Chengguo

Abstract

In this paper, we study optimal reinsurance design by minimizing the risk-adjusted value of an insurer’s liability, where the valuation is carried out by a cost-of-capital approach based either on the value at risk or the conditional value at risk. To prevent moral hazard and to be consistent with the spirit of reinsurance, we follow Vajda (1962) and assume that both the insurer’s retained loss and the proportion paid by a reinsurer are increasing in indemnity. We analyze the optimal solutions for a wide class of reinsurance premium principles which satisfy three axioms (law invariance, risk loading and preserving convex order) and encompass ten of the eleven widely used premium principles listed in Young (2004). Our results show that the optimal ceded loss functions are in the form of three interconnected line segments. Further simplified forms of the optimal reinsurance are obtained for the premium principles under an additional mild constraint. Finally, to illustrate the applicability of our results, we derive the optimal reinsurance explicitly for both the expected value principle and Wang’s principle.

Suggested Citation

  • Chi, Yichun & Weng, Chengguo, 2013. "Optimal reinsurance subject to Vajda condition," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 179-189.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:179-189
    DOI: 10.1016/j.insmatheco.2013.05.002
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    References listed on IDEAS

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    Cited by:

    1. Sun, Haoze & Weng, Chengguo & Zhang, Yi, 2017. "Optimal multivariate quota-share reinsurance: A nonparametric mean-CVaR framework," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 197-214.
    2. repec:spr:annopr:v:237:y:2016:i:1:d:10.1007_s10479-014-1584-8 is not listed on IDEAS
    3. Zhu, Yunzhou & Chi, Yichun & Weng, Chengguo, 2014. "Multivariate reinsurance designs for minimizing an insurer’s capital requirement," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 144-155.
    4. 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.
    5. Zheng, Yanting & Cui, Wei, 2014. "Optimal reinsurance with premium constraint under distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 109-120.
    6. Mi Chen & Wenyuan Wang & Ruixing Ming, 2016. "Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-12, December.

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