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Optimal reinsurance with general premium principles

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  • Chi, Yichun
  • Tan, Ken Seng

Abstract

In this paper, we study two classes of optimal reinsurance models from the perspective of an insurer by minimizing its total risk exposure under the criteria of value at risk (VaR) and conditional value at risk (CVaR), assuming that the reinsurance premium principles satisfy three basic axioms: distribution invariance, risk loading and stop-loss ordering preserving. The proposed class of premium principles is quite general in the sense that it encompasses eight of the eleven commonly used premium principles listed in Young (2004). Under the additional assumption that both the insurer and reinsurer are obligated to pay more for larger loss, we show that layer reinsurance is quite robust in the sense that it is always optimal over our assumed risk measures and the prescribed premium principles. We further use the Wang’s and Dutch premium principles to illustrate the applicability of our results by deriving explicitly the optimal parameters of the layer reinsurance. These two premium principles are chosen since in addition to satisfying the above three axioms, they exhibit increasing relative risk loading, a desirable property that is consistent with the market convention on reinsurance pricing.

Suggested Citation

  • Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
  • Handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:180-189
    DOI: 10.1016/j.insmatheco.2012.12.001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Nicole Bauerle & Alexander Glauner, 2017. "Optimal Risk Allocation in Reinsurance Networks," Papers 1711.10210, arXiv.org.
    2. 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.
    3. Hirbod Assa, 2014. "On Optimal Reinsurance Policy with Distortion Risk Measures and Premiums," Papers 1406.2950, arXiv.org.
    4. 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.
    5. Balbás, Alejandro & Balbás, Raquel & Balbás, Beatriz, 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).
    6. repec:eee:insuma:v:76:y:2017:i:c:p:185-195 is not listed on IDEAS
    7. repec:spr:annopr:v:237:y:2016:i:1:d:10.1007_s10479-014-1584-8 is not listed on IDEAS
    8. Wang, Ching-Ping & Huang, Hung-Hsi, 2016. "Optimal insurance contract under VaR and CVaR constraints," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 110-127.
    9. Brandtner, Mario & Kürsten, Wolfgang, 2014. "Solvency II, regulatory capital, and optimal reinsurance: How good are Conditional Value-at-Risk and spectral risk measures?," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 156-167.
    10. Alejandro Balbas & Beatriz Balbas & Raquel Balbas, 2013. "Optimal Reinsurance: A Risk Sharing Approach," Risks, MDPI, Open Access Journal, vol. 1(2), pages 1-12, August.
    11. Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
    12. repec:cys:ecocyb:v:50:y:2017:i:4:p:225-242 is not listed on IDEAS
    13. 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.
    14. Heras, Antonio & Balbas Aparicio, Raquel & Balbas Aparicio, Beatriz & Balbas de la Corte, Alejandro, 2014. "Optimal reinsurance under risk and uncertainty," INDEM - Working Paper Business Economic Series id-14-04, Instituto para el Desarrollo Empresarial (INDEM).
    15. Hirbod Assa, 2015. "Optimal risk allocation in a market with non-convex preferences," Papers 1503.04460, arXiv.org.
    16. 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.
    17. Tim J. Boonen, 2016. "Optimal Reinsurance with Heterogeneous Reference Probabilities," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-11, July.
    18. 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.
    19. Başak Bulut Karageyik & Şule Şahin, 2017. "Determination of the Optimal Retention Level Based on Different Measures," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(1), pages 1-21, January.
    20. Amir T. Payandeh Najafabadi & Ali Panahi Bazaz, 2017. "An Optimal Multi-layer Reinsurance Policy under Conditional Tail Expectation," Papers 1701.05447, arXiv.org.
    21. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "Convex ordering for insurance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 409-416.
    22. 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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